diff --git a/docs/release-notes/4076.feat.md b/docs/release-notes/4076.feat.md
new file mode 100644
index 0000000000..9a4938e420
--- /dev/null
+++ b/docs/release-notes/4076.feat.md
@@ -0,0 +1 @@
+Add preset support to {func}`scanpy.tl.diffmap`’s and {func}`scanpy.tl.draw_graph`’s `key_added` parameter {smaller}`P Angerer`
diff --git a/pyproject.toml b/pyproject.toml
index 16cf136060..bfcfd5555a 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -273,7 +273,8 @@ filterwarnings = [
     "ignore:FNV hashing is not implemented in Numba.*:UserWarning",
     # we want to see and eventually fix these
     "default::numba.core.errors.NumbaPerformanceWarning",
-    "default:.*TSNE.*random.*to.*pca:FutureWarning",                                    # we should set init=obsm["X_pca"] or so
+    # we should set init=obsm["X_pca"] or so
+    "default:.*TSNE.*random.*to.*pca:FutureWarning",
     # igraph vs leidenalg warning
     "ignore:The `igraph` implementation of leiden clustering:UserWarning",
     # everybody uses this zarr 3 feature, including us, XArray, lots of data out there …
diff --git a/src/scanpy/_settings/presets.py b/src/scanpy/_settings/presets.py
index 0119e821c1..c82d256147 100644
--- a/src/scanpy/_settings/presets.py
+++ b/src/scanpy/_settings/presets.py
@@ -76,10 +76,16 @@ class HVGPreset(NamedTuple):
     return_df: bool
 
 
-class PcaPreset(NamedTuple):
+class BasicEmbeddingPreset(NamedTuple):
     key_added: str | None
 
 
+# replace once they diverge
+PcaPreset = UmapPreset = TsnePreset = DiffmapPreset = DrawGraphPreset = (
+    BasicEmbeddingPreset
+)
+
+
 class RankGenesGroupsPreset(NamedTuple):
     method: DETest
     mask_var: str | None
@@ -193,6 +199,38 @@ def pca() -> Mapping[Preset, PcaPreset]:
             Preset.ScanpyV2Preview: PcaPreset(key_added="pca"),
         }
 
+    @preset_property
+    def umap() -> Mapping[Preset, UmapPreset]:
+        """Settings for :func:`~scanpy.tl.umap`."""  # noqa: D401
+        return {
+            Preset.ScanpyV1: DiffmapPreset(key_added=None),
+            Preset.ScanpyV2Preview: DiffmapPreset(key_added="umap"),
+        }
+
+    @preset_property
+    def tsne() -> Mapping[Preset, UmapPreset]:
+        """Settings for :func:`~scanpy.tl.tsne`."""  # noqa: D401
+        return {
+            Preset.ScanpyV1: DiffmapPreset(key_added=None),
+            Preset.ScanpyV2Preview: DiffmapPreset(key_added="tsne"),
+        }
+
+    @preset_property
+    def diffmap() -> Mapping[Preset, DiffmapPreset]:
+        """Settings for :func:`~scanpy.tl.diffmap`."""  # noqa: D401
+        return {
+            Preset.ScanpyV1: DiffmapPreset(key_added=None),
+            Preset.ScanpyV2Preview: DiffmapPreset(key_added="diffmap"),
+        }
+
+    @preset_property
+    def draw_graph() -> Mapping[Preset, DrawGraphPreset]:
+        """Settings for :func:`~scanpy.tl.draw_graph`."""  # noqa: D401
+        return {
+            Preset.ScanpyV1: DrawGraphPreset(key_added=None),
+            Preset.ScanpyV2Preview: DrawGraphPreset(key_added="graph_{layout}"),
+        }
+
     @preset_property
     def rank_genes_groups() -> Mapping[Preset, RankGenesGroupsPreset]:
         """Correlation method for :func:`~scanpy.tl.rank_genes_groups`."""
diff --git a/src/scanpy/_utils/__init__.py b/src/scanpy/_utils/__init__.py
index f0d67b550d..68033aec71 100644
--- a/src/scanpy/_utils/__init__.py
+++ b/src/scanpy/_utils/__init__.py
@@ -39,7 +39,7 @@
 if TYPE_CHECKING:
     from collections.abc import Callable, Iterable, KeysView, Mapping
     from pathlib import Path
-    from typing import Any
+    from typing import Any, Concatenate
 
     from anndata import AnnData
     from igraph import Graph
@@ -47,6 +47,7 @@
     from pandas._typing import Dtype as PdDtype
 
     from .._compat import CSRBase
+    from .._settings import Preset
     from ..neighbors import NeighborsParams, RPForestDict
 
     type _MemoryArray = NDArray | CSBase
@@ -58,6 +59,8 @@
     "NeighborsView",
     "_choose_graph",
     "_doc_params",
+    "_existing_preset_keys",
+    "_get_basis",
     "_numba_thread_limit",
     "_resolve_axis",
     "annotate_doc_types",
@@ -573,6 +576,29 @@ def get_literal_vals(typ: UnionType | TypeAliasType | Any) -> KeysView[Any]:
     raise TypeError(msg)
 
 
+def _get_basis_key(adata: AnnData, basis: str) -> str | None:
+    if basis in adata.obsm:
+        return basis
+    if f"X_{basis}" in adata.obsm:
+        return f"X_{basis}"
+    return None
+
+
+def _existing_preset_keys[**P, T: tuple[str, ...]](
+    adata: AnnData,
+    keys: Callable[Concatenate[Preset, P], T],
+    *args: P.args,
+    **kw: P.kwargs,
+) -> T | None:
+    from .._settings import Preset
+
+    for preset in (Preset.ScanpyV1, Preset.ScanpyV2Preview):
+        obsm_key, *rest = keys(preset, *args, **kw)
+        if obsm_key in adata.obsm:
+            return (obsm_key, *rest)
+    return None
+
+
 # --------------------------------------------------------------------------------
 # Others
 # --------------------------------------------------------------------------------
diff --git a/src/scanpy/experimental/pp/_normalization.py b/src/scanpy/experimental/pp/_normalization.py
index 551df22be4..49c516eaba 100644
--- a/src/scanpy/experimental/pp/_normalization.py
+++ b/src/scanpy/experimental/pp/_normalization.py
@@ -7,6 +7,7 @@
 from anndata import AnnData
 
 from ... import logging as logg
+from ... import settings
 from ..._compat import CSBase, warn
 from ..._settings import Default
 from ..._utils import _doc_params, check_nonnegative_integers, view_to_actual
@@ -22,7 +23,7 @@
 )
 from ...get import _check_mask, _get_obs_rep, _set_obs_rep
 from ...preprocessing._docs import doc_mask_var
-from ...preprocessing._pca import pca
+from ...preprocessing._pca import _pca_keys, pca
 
 if TYPE_CHECKING:
     from collections.abc import Mapping
@@ -207,19 +208,21 @@ def normalize_pearson_residuals_pca(
     `.uns['pearson_residuals_normalization']['clip']`
         The used value of the clipping parameter.
 
-    `.obsm['X_pca']`
+    `.obsm[kwargs_pca.get('key_added', 'X_pca')]`
         PCA representation of data after gene selection (if applicable) and Pearson
         residual normalization.
-    `.varm['PCs']`
+    `.varm[kwargs_pca.get('key_added', 'PCs')]`
         The principal components containing the loadings. When `inplace=True` and
         `mask_var is not None`, this will contain empty rows for the genes not
         selected.
-    `.uns['pca']['variance_ratio']`
+    `.uns[kwargs_pca.get('key_added', 'pca')]['variance_ratio']`
         Ratio of explained variance.
-    `.uns['pca']['variance']`
+    `.uns[kwargs_pca.get('key_added', 'pca')]['variance']`
         Explained variance, equivalent to the eigenvalues of the covariance matrix.
 
     """
+    key_added = kwargs_pca.get("key_added", settings.preset.pca.key_added)
+    key_obsm, key_varm, key_uns = _pca_keys(key_added)
     if isinstance(mask_var, Default):
         mask_var = "highly_variable" if "highly_variable" in adata.var else None
     mask_var = _check_mask(adata, mask_var, "var")
@@ -236,19 +239,19 @@ def normalize_pearson_residuals_pca(
         adata_pca, theta=theta, clip=clip, check_values=check_values
     )
     pca(adata_pca, n_comps=n_comps, rng=rng, **kwargs_pca)
-    n_comps = adata_pca.obsm["X_pca"].shape[1]  # might be None
+    n_comps = adata_pca.obsm[key_obsm].shape[1]  # might be None
 
     if inplace:
         norm_settings = adata_pca.uns["pearson_residuals_normalization"]
         norm_dict = dict(**norm_settings, pearson_residuals_df=adata_pca.to_df())
         if mask_var is not None:
-            adata.varm["PCs"] = np.zeros(shape=(adata.n_vars, n_comps))
-            adata.varm["PCs"][mask_var] = adata_pca.varm["PCs"]
+            adata.varm[key_varm] = np.zeros(shape=(adata.n_vars, n_comps))
+            adata.varm[key_varm][mask_var] = adata_pca.varm[key_varm]
         else:
-            adata.varm["PCs"] = adata_pca.varm["PCs"]
-        adata.uns["pca"] = adata_pca.uns["pca"]
+            adata.varm[key_varm] = adata_pca.varm[key_varm]
+        adata.uns[key_uns] = adata_pca.uns[key_uns]
         adata.uns["pearson_residuals_normalization"] = norm_dict
-        adata.obsm["X_pca"] = adata_pca.obsm["X_pca"]
+        adata.obsm[key_obsm] = adata_pca.obsm[key_obsm]
         return None
     else:
         return adata_pca
diff --git a/src/scanpy/experimental/pp/_recipes.py b/src/scanpy/experimental/pp/_recipes.py
index 61db8e8a5e..f0f63d0069 100644
--- a/src/scanpy/experimental/pp/_recipes.py
+++ b/src/scanpy/experimental/pp/_recipes.py
@@ -5,7 +5,7 @@
 
 import numpy as np
 
-from ... import experimental
+from ... import experimental, settings
 from ..._utils import _doc_params
 from ..._utils.random import _accepts_legacy_random_state
 from ...experimental._docs import (
@@ -17,6 +17,7 @@
     doc_pca_chunk,
 )
 from ...preprocessing import pca
+from ...preprocessing._pca import _pca_keys
 
 if TYPE_CHECKING:
     from collections.abc import Mapping
@@ -103,18 +104,20 @@ def recipe_pearson_residuals(  # noqa: PLR0913
     `.uns['pearson_residuals_normalization']['clip']`
          The used value of the clipping parameter.
 
-    `.obsm['X_pca']`
+    `.obsm[kwargs_pca.get('key_added', 'X_pca')]`
         PCA representation of data after gene selection and Pearson residual
         normalization.
-    `.varm['PCs']`
+    `.varm[kwargs_pca.get('key_added', 'PCs')]`
          The principal components containing the loadings. When `inplace=True` this
          will contain empty rows for the genes not selected during HVG selection.
-    `.uns['pca']['variance_ratio']`
+    `.uns[kwargs_pca.get('key_added', 'pca')]['variance_ratio']`
          Ratio of explained variance.
-    `.uns['pca']['variance']`
+    `.uns[kwargs_pca.get('key_added', 'pca')]['variance']`
          Explained variance, equivalent to the eigenvalues of the covariance matrix.
 
     """
+    key_added = kwargs_pca.get("key_added", settings.preset.pca.key_added)
+    key_obsm, key_varm, key_uns = _pca_keys(key_added)
     hvg_args = dict(
         flavor="pearson_residuals",
         n_top_genes=n_top_genes,
@@ -145,11 +148,11 @@ def recipe_pearson_residuals(  # noqa: PLR0913
             **normalization_param, pearson_residuals_df=adata_pca.to_df()
         )
 
-        adata.uns["pca"] = adata_pca.uns["pca"]
-        adata.varm["PCs"] = np.zeros(shape=(adata.n_vars, n_comps))
-        adata.varm["PCs"][adata.var["highly_variable"]] = adata_pca.varm["PCs"]
+        adata.uns[key_uns] = adata_pca.uns[key_uns]
+        adata.varm[key_varm] = np.zeros(shape=(adata.n_vars, n_comps))
+        adata.varm[key_varm][adata.var["highly_variable"]] = adata_pca.varm[key_varm]
         adata.uns["pearson_residuals_normalization"] = normalization_dict
-        adata.obsm["X_pca"] = adata_pca.obsm["X_pca"]
+        adata.obsm[key_obsm] = adata_pca.obsm[key_obsm]
         return None
     else:
         return adata_pca, hvg
diff --git a/src/scanpy/external/exporting.py b/src/scanpy/external/exporting.py
index 55d39eb2b2..076153b822 100644
--- a/src/scanpy/external/exporting.py
+++ b/src/scanpy/external/exporting.py
@@ -14,7 +14,9 @@
 from fast_array_utils.stats import mean_var
 from pandas.api.types import CategoricalDtype
 
-from .._utils import NeighborsView
+from .._utils import NeighborsView, _existing_preset_keys
+from ..preprocessing._pca import _pca_keys
+from ..tools._draw_graph import _draw_graph_keys
 
 if TYPE_CHECKING:
     from collections.abc import Iterable, Mapping
@@ -81,8 +83,12 @@ def spring_project(  # noqa: PLR0912, PLR0915
     if embedding_method not in adata.obsm:
         if f"X_{embedding_method}" in adata.obsm:
             embedding_method = f"X_{embedding_method}"
-        elif embedding_method in adata.uns:
-            embedding_method = f"X_{embedding_method}_{adata.uns[embedding_method]['params']['layout']}"
+        elif embedding_method in {"graph", "draw_graph"} and (
+            keys := _existing_preset_keys(
+                adata, _draw_graph_keys, adata.uns[embedding_method]["params"]["layout"]
+            )
+        ):
+            embedding_method = keys[0]
         else:
             msg = f"Run the specified embedding method `{embedding_method}` first."
             raise ValueError(msg)
@@ -222,10 +228,10 @@ def spring_project(  # noqa: PLR0912, PLR0915
     )
 
     # Write some useful intermediates, if they exist
-    if "X_pca" in adata.obsm:
+    if keys := _existing_preset_keys(adata, _pca_keys):
         np.savez_compressed(
             subplot_dir / "intermediates.npz",
-            Epca=adata.obsm["X_pca"],
+            Epca=adata.obsm[keys[0]],
             total_counts=total_counts,
         )
 
diff --git a/src/scanpy/external/tl/_trimap.py b/src/scanpy/external/tl/_trimap.py
index 8ccd08f1f3..922c792a8d 100644
--- a/src/scanpy/external/tl/_trimap.py
+++ b/src/scanpy/external/tl/_trimap.py
@@ -7,7 +7,9 @@
 from ... import logging as logg
 from ..._compat import CSBase
 from ..._settings import settings
+from ..._utils import _existing_preset_keys
 from ..._utils._doctests import doctest_needs
+from ...preprocessing._pca import _pca_keys
 
 if TYPE_CHECKING:
     from typing import Literal
@@ -100,9 +102,9 @@ def trimap(  # noqa: PLR0913
     verbosity = settings.verbosity if verbose is None else verbose
     verbose = verbosity if isinstance(verbosity, bool) else verbosity > 0
 
-    if "X_pca" in adata.obsm:
-        n_dim_pca = adata.obsm["X_pca"].shape[1]
-        x = adata.obsm["X_pca"][:, : min(n_dim_pca, 100)]
+    if keys := _existing_preset_keys(adata, _pca_keys):
+        n_dim_pca = adata.obsm[keys[0]].shape[1]
+        x = adata.obsm[keys[0]][:, : min(n_dim_pca, 100)]
     else:
         x = adata.X
         if isinstance(x, CSBase):
@@ -111,7 +113,7 @@ def trimap(  # noqa: PLR0913
                 "use a dense matrix or apply pca first."
             )
             raise ValueError(msg)
-        logg.warning("`X_pca` not found. Run `sc.pp.pca` first for speedup.")
+        logg.warning("`pca`/`X_pca` not found. Run `sc.pp.pca` first for speedup.")
     x_trimap = TRIMAP(
         n_dims=n_components,
         n_inliers=n_inliers,
diff --git a/src/scanpy/neighbors/__init__.py b/src/scanpy/neighbors/__init__.py
index 7bc2470df3..a9c838b949 100644
--- a/src/scanpy/neighbors/__init__.py
+++ b/src/scanpy/neighbors/__init__.py
@@ -18,7 +18,7 @@
 from .._compat import CSBase, CSRBase, SpBase, pkg_version, warn
 from .._docs import doc_rng
 from .._settings import settings
-from .._utils import NeighborsView, _doc_params, get_literal_vals
+from .._utils import NeighborsView, _doc_params, _existing_preset_keys, get_literal_vals
 from .._utils.random import (
     _accepts_legacy_random_state,
     _legacy_random_state,
@@ -322,20 +322,6 @@ class FlatTree(NamedTuple):  # noqa: D101
     indices: None
 
 
-def _backwards_compat_get_full_x_diffmap(adata: AnnData) -> np.ndarray:
-    if "X_diffmap0" in adata.obs:
-        return np.c_[adata.obs["X_diffmap0"].values[:, None], adata.obsm["X_diffmap"]]
-    else:
-        return adata.obsm["X_diffmap"]
-
-
-def _backwards_compat_get_full_eval(adata: AnnData):
-    if "X_diffmap0" in adata.obs:
-        return np.r_[1, adata.uns["diffmap_evals"]]
-    else:
-        return adata.uns["diffmap_evals"]
-
-
 def _make_forest_dict(forest):
     d = {}
     props = ("hyperplanes", "offsets", "children", "indices")
@@ -432,6 +418,7 @@ def __init__(  # noqa: PLR0912, PLR0915
         *,
         n_dcs: int | None = None,
         neighbors_key: str | None = None,
+        diffmap_key: str | None = None,
     ) -> None:
         self._adata = adata
         self._init_iroot()
@@ -484,9 +471,16 @@ def count_nonzero(a: np.ndarray | CSRBase) -> int:
 
                 self._connected_components = connected_components(self._connectivities)
                 self._number_connected_components = self._connected_components[0]
-        if "X_diffmap" in adata.obsm:
-            self._eigen_values = _backwards_compat_get_full_eval(adata)
-            self._eigen_basis = _backwards_compat_get_full_x_diffmap(adata)
+
+        from ..tools._dpt import _diffmap_keys
+
+        if keys := (
+            (diffmap_key, diffmap_key)
+            if diffmap_key
+            else _existing_preset_keys(adata, _diffmap_keys)
+        ):
+            self._eigen_values = adata.uns[keys[1]]
+            self._eigen_basis = adata.obsm[keys[0]]
             if n_dcs is not None:
                 if n_dcs > len(self._eigen_values):
                     msg = (
diff --git a/src/scanpy/plotting/_tools/__init__.py b/src/scanpy/plotting/_tools/__init__.py
index e41f4ea908..bba09e85ce 100644
--- a/src/scanpy/plotting/_tools/__init__.py
+++ b/src/scanpy/plotting/_tools/__init__.py
@@ -13,7 +13,7 @@
 
 from ... import logging as logg
 from ..._settings import Default, settings
-from ..._utils import _doc_params, sanitize_anndata, with_cat_dtype
+from ..._utils import _doc_params, _get_basis_key, sanitize_anndata, with_cat_dtype
 from ..._utils.random import _LegacyRng
 from ...get import obs_df, rank_genes_groups_df
 from .._anndata import ranking
@@ -1495,9 +1495,9 @@ def embedding_density(  # noqa: PLR0912, PLR0913, PLR0915
     if groupby is not None:
         key += f"_{groupby}"
 
-    if f"X_{basis}" not in adata.obsm:
+    if _get_basis_key(adata, basis) is None:
         msg = (
-            f"Cannot find the embedded representation `adata.obsm['X_{basis}']`. "
+            f"Cannot find the embedded representation `adata.obsm[{basis!r} | 'X_{basis}']`. "
             "Compute the embedding first."
         )
         raise ValueError(msg)
diff --git a/src/scanpy/plotting/_tools/paga.py b/src/scanpy/plotting/_tools/paga.py
index d5100f1338..f8cfb6bd25 100644
--- a/src/scanpy/plotting/_tools/paga.py
+++ b/src/scanpy/plotting/_tools/paga.py
@@ -129,7 +129,7 @@ def paga_compare(  # noqa: PLR0912, PLR0913
         else:
             basis = "umap"
 
-    from .scatterplots import _components_to_dimensions, _get_basis, embedding
+    from .scatterplots import _components_to_dimensions, _get_basis_arr, embedding
 
     embedding(
         adata,
@@ -156,7 +156,7 @@ def paga_compare(  # noqa: PLR0912, PLR0913
     if pos is None:
         if color == adata.uns["paga"]["groups"]:
             # TODO: Use dimensions here
-            _basis = _get_basis(adata, basis)
+            _basis = _get_basis_arr(adata, basis)
             dims = _components_to_dimensions(
                 components=components, dimensions=None, total_dims=_basis.shape[1]
             )[0]
diff --git a/src/scanpy/plotting/_tools/scatterplots.py b/src/scanpy/plotting/_tools/scatterplots.py
index e18305140f..a7a83a517e 100644
--- a/src/scanpy/plotting/_tools/scatterplots.py
+++ b/src/scanpy/plotting/_tools/scatterplots.py
@@ -19,9 +19,16 @@
 
 from ... import logging as logg
 from ..._settings import Default, settings
-from ..._utils import _doc_params, sanitize_anndata
+from ..._utils import (
+    _doc_params,
+    _existing_preset_keys,
+    _get_basis_key,
+    sanitize_anndata,
+)
 from ..._utils._doctests import doctest_internet
 from ...get import _check_mask
+from ...preprocessing._pca import _pca_keys
+from ...tools._draw_graph import _draw_graph_keys
 from .. import _utils
 from .._docs import (
     doc_adata_color_etc,
@@ -147,7 +154,7 @@ def embedding(  # noqa: PLR0912, PLR0913, PLR0915
     check_projection(projection)
     sanitize_anndata(adata)
 
-    basis_values = _get_basis(adata, basis)
+    basis_values = _get_basis_arr(adata, basis)
     dimensions = _components_to_dimensions(
         components, dimensions, projection=projection, total_dims=basis_values.shape[1]
     )
@@ -852,12 +859,10 @@ def draw_graph(
     """
     if layout is None:
         layout = str(adata.uns["draw_graph"]["params"]["layout"])
-    basis = f"draw_graph_{layout}"
-    if f"X_{basis}" not in adata.obsm:
-        msg = f"Did not find {basis} in adata.obs. Did you compute layout {layout}?"
-        raise ValueError(msg)
-
-    return embedding(adata, basis, **kwargs)
+    if keys := _existing_preset_keys(adata, _draw_graph_keys, layout):
+        return embedding(adata, keys[0], **kwargs)
+    msg = f"Did not find `adata.obsm['draw_graph_{layout}']`. Did you compute layout {layout}?"
+    raise ValueError(msg)
 
 
 @_wraps_plot_scatter
@@ -925,7 +930,7 @@ def pca(
         return embedding(
             adata, "pca", show=show, return_fig=return_fig, save=save, **kwargs
         )
-    if "pca" not in adata.obsm and "X_pca" not in adata.obsm:
+    if not _existing_preset_keys(adata, _pca_keys):
         msg = (
             f"Could not find entry in `obsm` for 'pca'.\n"
             f"Available keys are: {list(adata.obsm.keys())}."
@@ -1202,15 +1207,12 @@ def _add_categorical_legend(  # noqa: PLR0913
             ax.legend(loc=legend_loc, fontsize=legend_fontsize)
 
 
-def _get_basis(adata: AnnData, basis: str) -> np.ndarray:
+def _get_basis_arr(adata: AnnData, basis: str) -> np.ndarray:
     """Get array for basis from anndata. Just tries to add 'X_'."""
-    if basis in adata.obsm:
-        return adata.obsm[basis]
-    elif f"X_{basis}" in adata.obsm:
-        return adata.obsm[f"X_{basis}"]
-    else:
-        msg = f"Could not find {basis!r} or 'X_{basis}' in .obsm"
-        raise KeyError(msg)
+    if basis_key := _get_basis_key(adata, basis):
+        return adata.obsm[basis_key]
+    msg = f"Could not find {basis!r} or 'X_{basis}' in .obsm"
+    raise KeyError(msg)
 
 
 def _get_color_source_vector(
diff --git a/src/scanpy/plotting/_utils.py b/src/scanpy/plotting/_utils.py
index 23cad1c111..c43c3fea97 100644
--- a/src/scanpy/plotting/_utils.py
+++ b/src/scanpy/plotting/_utils.py
@@ -18,7 +18,7 @@
 from .. import logging as logg
 from .._compat import warn
 from .._settings import Default, settings
-from .._utils import NeighborsView
+from .._utils import NeighborsView, _get_basis_key
 from . import palettes
 
 if TYPE_CHECKING:
@@ -567,7 +567,7 @@ def plot_edges(axs, adata, basis, edges_width, edges_color, *, neighbors_key=Non
         raise ValueError(msg)
     neighbors = NeighborsView(adata, neighbors_key)
     g = nx.Graph(neighbors["connectivities"])
-    basis_key = _get_basis(adata, basis)
+    basis_key = _get_basis_key(adata, basis)
 
     with warnings.catch_warnings():
         warnings.simplefilter("ignore")
@@ -602,7 +602,7 @@ def plot_arrows(axs, adata, basis, arrows_kwds=None):
             "Prefer using `scv.pl.velocity_embedding` to `arrows=True`."
         )
 
-    basis_key = _get_basis(adata, basis)
+    basis_key = _get_basis_key(adata, basis)
     x = adata.obsm[basis_key]
     v = adata.obsm[f"{v_prefix}_{basis}"]
     for ax in axs:
@@ -1027,16 +1027,6 @@ def fix_kwds(kwds_dict, **kwargs):
     return kwargs
 
 
-def _get_basis(adata: AnnData, basis: str):
-    if basis in adata.obsm:
-        basis_key = basis
-
-    elif f"X_{basis}" in adata.obsm:
-        basis_key = f"X_{basis}"
-
-    return basis_key
-
-
 def check_colornorm(vmin=None, vmax=None, vcenter=None, norm=None):
     from matplotlib.colors import Normalize
 
diff --git a/src/scanpy/preprocessing/_pca/__init__.py b/src/scanpy/preprocessing/_pca/__init__.py
index 4f7a267e15..52741a2c3a 100644
--- a/src/scanpy/preprocessing/_pca/__init__.py
+++ b/src/scanpy/preprocessing/_pca/__init__.py
@@ -8,7 +8,7 @@
 from ... import logging as logg
 from ..._compat import CSBase, DaskArray, warn
 from ..._docs import doc_rng
-from ..._settings import Default, settings
+from ..._settings import Default, Preset, settings
 from ..._utils import _doc_params, get_literal_vals, is_backed_type
 from ..._utils.random import _accepts_legacy_random_state, _legacy_random_state
 from ...get import _check_mask, _get_obs_rep
@@ -47,6 +47,20 @@
 type SvdSolver = SvdSolvDaskML | SvdSolvSkearn | SvdSolvPCACustom
 
 
+def _pca_keys(
+    key_added: str | None | Default | Preset = Default(),
+) -> tuple[str, str, str]:
+    if isinstance(key_added, Default):
+        key_added = settings.preset
+    if isinstance(key_added, Preset):
+        key_added = key_added.pca.key_added
+    return (
+        ("X_pca", "PCs", "pca")
+        if key_added is None
+        else (key_added, key_added, key_added)
+    )
+
+
 @_doc_params(mask_var=doc_mask_var, rng=doc_rng)
 @_accepts_legacy_random_state(0)
 def pca(  # noqa: PLR0912, PLR0913, PLR0915
@@ -203,8 +217,6 @@ def pca(  # noqa: PLR0912, PLR0913, PLR0915
         # Current chunking implementation relies on pca being called on X
         msg = "Cannot use `layer`/`obsm` and `chunked` at the same time."
         raise NotImplementedError(msg)
-    if isinstance(key_added, Default):
-        key_added = settings.preset.pca.key_added
 
     # chunked calculation is not randomized, anyways
     if svd_solver in {"auto", "randomized"} and not chunked:
@@ -337,9 +349,7 @@ def pca(  # noqa: PLR0912, PLR0913, PLR0915
         x_pca = x_pca.astype(dtype)
 
     if return_anndata:
-        key_obsm, key_varm, key_uns = (
-            ("X_pca", "PCs", "pca") if key_added is None else [key_added] * 3
-        )
+        key_obsm, key_varm, key_uns = _pca_keys(key_added)
         adata.obsm[key_obsm] = x_pca
 
         if obsm:
diff --git a/src/scanpy/tools/_diffmap.py b/src/scanpy/tools/_diffmap.py
index 90f2976837..0d03ee9bdc 100644
--- a/src/scanpy/tools/_diffmap.py
+++ b/src/scanpy/tools/_diffmap.py
@@ -5,6 +5,7 @@
 import numpy as np
 
 from .._docs import doc_rng
+from .._settings import Default
 from .._utils import _doc_params
 from .._utils.random import _accepts_legacy_random_state
 from ._dpt import _diffmap
@@ -22,6 +23,7 @@ def diffmap(
     n_comps: int = 15,
     *,
     neighbors_key: str | None = None,
+    key_added: str | None | Default = Default(preset=("diffmap", "key_added")),
     rng: SeedLike | RNGLike | None = None,
     copy: bool = False,
 ) -> AnnData | None:
@@ -55,6 +57,8 @@ def diffmap(
         .obsp[.uns[neighbors_key]['connectivities_key']] and
         .obsp[.uns[neighbors_key]['distances_key']] for connectivities and distances,
         respectively.
+    key_added
+        Control where the embedding and eigenvalues are stored.
     {rng}
     copy
         Return a copy instead of writing to adata.
@@ -63,11 +67,11 @@ def diffmap(
     -------
     Returns `None` if `copy=False`, else returns an `AnnData` object. Sets the following fields:
 
-    `adata.obsm['X_diffmap']` : :class:`numpy.ndarray` (dtype `float`)
+    `adata.obsm['X_diffmap' | key_added]` : :class:`numpy.ndarray` (dtype `float`)
         Diffusion map representation of data, which is the right eigen basis of
         the transition matrix with eigenvectors as columns.
 
-    `adata.uns['diffmap_evals']` : :class:`numpy.ndarray` (dtype `float`)
+    `adata.uns['diffmap_evals' | key_added]` : :class:`numpy.ndarray` (dtype `float`)
         Array of size (number of eigen vectors).
         Eigenvalues of transition matrix.
 
@@ -90,5 +94,11 @@ def diffmap(
         msg = "Provide any value greater than 2 for `n_comps`. "
         raise ValueError(msg)
     adata = adata.copy() if copy else adata
-    _diffmap(adata, n_comps=n_comps, neighbors_key=neighbors_key, rng=rng)
+    _diffmap(
+        adata,
+        n_comps=n_comps,
+        neighbors_key=neighbors_key,
+        key_added=key_added,
+        rng=rng,
+    )
     return adata if copy else None
diff --git a/src/scanpy/tools/_dpt.py b/src/scanpy/tools/_dpt.py
index 74d7fe66ae..f97cc98eef 100644
--- a/src/scanpy/tools/_dpt.py
+++ b/src/scanpy/tools/_dpt.py
@@ -7,8 +7,11 @@
 import scipy as sp
 from natsort import natsorted
 
+from scanpy._utils.random import _LegacyRng
+from scanpy.tools._utils import _existing_preset_keys
+
 from .. import logging as logg
-from .._utils.random import _LegacyRng
+from .._settings import Default, Preset, settings
 from ..neighbors import Neighbors, OnFlySymMatrix
 
 if TYPE_CHECKING:
@@ -17,26 +20,38 @@
     from anndata import AnnData
 
 
+def _diffmap_keys(key_added: str | None | Default | Preset) -> tuple[str, str]:
+    if isinstance(key_added, Default):
+        key_added = settings.preset
+    if isinstance(key_added, Preset):
+        key_added = key_added.diffmap.key_added
+    return (
+        ("X_diffmap", "diffmap_evals") if key_added is None else (key_added, key_added)
+    )
+
+
 def _diffmap(
     adata: AnnData,
     n_comps: int = 15,
     *,
     neighbors_key: str | None,
+    key_added: str | None | Default,
     rng: np.random.Generator,
 ) -> None:
+    obsm_key, uns_key = _diffmap_keys(key_added)
     start = logg.info(f"computing Diffusion Maps using {n_comps=}(=n_dcs)")
     dpt = DPT(adata, neighbors_key=neighbors_key)
     dpt.compute_transitions()
     dpt.compute_eigen(n_comps=n_comps, rng=rng)
-    adata.obsm["X_diffmap"] = dpt.eigen_basis
-    adata.uns["diffmap_evals"] = dpt.eigen_values
+    adata.obsm[obsm_key] = dpt.eigen_basis
+    adata.uns[uns_key] = dpt.eigen_values
     logg.info(
         "    finished",
         time=start,
         deep=(
             "added\n"
-            "    'X_diffmap', diffmap coordinates (adata.obsm)\n"
-            "    'diffmap_evals', eigenvalues of transition matrix (adata.uns)"
+            f"    {obsm_key!r}, diffmap coordinates (adata.obsm)\n"
+            f"    {uns_key!r}, eigenvalues of transition matrix (adata.uns)"
         ),
     )
 
@@ -49,6 +64,7 @@ def dpt(
     min_group_size: float = 0.01,
     allow_kendall_tau_shift: bool = True,
     neighbors_key: str | None = None,
+    diffmap_key: str | None = None,
     copy: bool = False,
 ) -> AnnData | None:
     """Infer progression of cells through geodesic distance along the graph :cite:p:`Haghverdi2016,Wolf2019`.
@@ -106,6 +122,9 @@ def dpt(
         .obsp[.uns[neighbors_key]['connectivities_key']] and
         .obsp[.uns[neighbors_key]['distances_key']] for connectivities and distances,
         respectively.
+    diffmap_key
+        If specified, dpt looks in .obsm[diffmap_key] for diffmap coordinates,
+        otherwise int the default place.
     copy
         Copy instance before computation and return a copy.
         Otherwise, perform computation inplace and return `None`.
@@ -142,12 +161,14 @@ def dpt(
             "    adata.uns['iroot'] = root_cell_index\n"
             "    adata.var['xroot'] = adata[root_cell_name, :].X"
         )
-    if "X_diffmap" not in adata.obsm:
+    if not diffmap_key and not _existing_preset_keys(adata, _diffmap_keys):
         logg.warning(
             "Trying to run `tl.dpt` without prior call of `tl.diffmap`. "
             "Falling back to `tl.diffmap` with default parameters."
         )
-        _diffmap(adata, neighbors_key=neighbors_key, rng=_LegacyRng(0))
+        from ._diffmap import diffmap
+
+        diffmap(adata, neighbors_key=neighbors_key, rng=_LegacyRng(0))
     # start with the actual computation
     dpt = DPT(
         adata,
@@ -156,6 +177,7 @@ def dpt(
         n_branchings=n_branchings,
         allow_kendall_tau_shift=allow_kendall_tau_shift,
         neighbors_key=neighbors_key,
+        diffmap_key=diffmap_key,
     )
     start = logg.info(f"computing Diffusion Pseudotime using {n_dcs=}")
     if n_branchings > 1:
@@ -216,8 +238,11 @@ def __init__(
         n_branchings: int = 0,
         allow_kendall_tau_shift: bool = False,
         neighbors_key: str | None = None,
+        diffmap_key: str | None = None,
     ):
-        super().__init__(adata, n_dcs=n_dcs, neighbors_key=neighbors_key)
+        super().__init__(
+            adata, n_dcs=n_dcs, neighbors_key=neighbors_key, diffmap_key=diffmap_key
+        )
         self.flavor = "haghverdi16"
         self.n_branchings = n_branchings
         self.min_group_size = (
diff --git a/src/scanpy/tools/_draw_graph.py b/src/scanpy/tools/_draw_graph.py
index ae209599d1..ace03145a0 100644
--- a/src/scanpy/tools/_draw_graph.py
+++ b/src/scanpy/tools/_draw_graph.py
@@ -7,7 +7,9 @@
 
 from .. import _utils
 from .. import logging as logg
+from .._compat import warn
 from .._docs import doc_rng
+from .._settings import Default, Preset, settings
 from .._utils import _choose_graph, _doc_params, get_literal_vals
 from .._utils.random import (
     _accepts_legacy_random_state,
@@ -42,10 +44,12 @@ def draw_graph(  # noqa: PLR0913
     rng: SeedLike | RNGLike | None = None,
     n_jobs: int | None = None,
     adjacency: CSBase | None = None,
-    key_added_ext: str | None = None,
+    key_added: str | None | Default = Default(preset=("draw_graph", "key_added")),
     neighbors_key: str | None = None,
     obsp: str | None = None,
     copy: bool = False,
+    # deprecated
+    key_added_ext: str | None = None,
     **kwds,
 ) -> AnnData | None:
     """Force-directed graph drawing :cite:p:`Islam2011,Jacomy2014,Chippada2018`.
@@ -86,21 +90,21 @@ def draw_graph(  # noqa: PLR0913
         Applies to layouts with random initialization like `'fr'`.
     adjacency
         Sparse adjacency matrix of the graph, defaults to neighbors connectivities.
-    key_added_ext
-        By default, append `layout`.
+    key_added
+        Template for the key. If `None`, uses `f'X_draw_graph_{{layout}}'` for `obsm`.
     proceed
-        Continue computation, starting off with 'X_draw_graph_`layout`'.
+        Continue computation, starting off with `f'X_draw_graph_{{layout}}'`.
     init_pos
         `'paga'`/`True`, `None`/`False`, or any valid 2d-`.obsm` key.
         Use precomputed coordinates for initialization.
         If `False`/`None` (the default), initialize randomly.
     neighbors_key
-        If not specified, draw_graph looks at .obsp['connectivities'] for connectivities
+        If not specified, draw_graph looks at `.obsp['connectivities']` for connectivities
         (default storage place for pp.neighbors).
         If specified, draw_graph looks at
-        .obsp[.uns[neighbors_key]['connectivities_key']] for connectivities.
+        `.obsp[.uns[neighbors_key]['connectivities_key']]` for connectivities.
     obsp
-        Use .obsp[obsp] as adjacency. You can't specify both
+        Use `.obsp[obsp]` as adjacency. You can't specify both
         `obsp` and `neighbors_key` at the same time.
     copy
         Return a copy instead of writing to adata.
@@ -113,7 +117,7 @@ def draw_graph(  # noqa: PLR0913
     -------
     Returns `None` if `copy=False`, else returns an `AnnData` object. Sets the following fields:
 
-    `adata.obsm['X_draw_graph_[layout | key_added_ext]']` : :class:`numpy.ndarray` (dtype `float`)
+    `adata.obsm[(f'X_draw_graph_{{layout}}' | key_added).format(layout=layout)]` : :class:`numpy.ndarray` (dtype `float`)
         Coordinates of graph layout. E.g. for `layout='fa'` (the default),
         the field is called `'X_draw_graph_fa'`. `key_added_ext` overwrites `layout`.
     `adata.uns['draw_graph']`: :class:`dict`
@@ -121,6 +125,8 @@ def draw_graph(  # noqa: PLR0913
 
     """
     start = logg.info(f"drawing single-cell graph using layout {layout!r}")
+    layout = coerce_fa2_layout(layout)
+    key_obsm, key_uns = _draw_graph_keys(key_added, layout, key_added_ext)
     rng = np.random.default_rng(rng)
     meta_random_state = (
         dict(random_state=rng.arg) if isinstance(rng, _LegacyRng) else {}
@@ -145,7 +151,6 @@ def draw_graph(  # noqa: PLR0913
     else:
         _if_legacy_apply_global(rng)
         init_coords = rng.random((adjacency.shape[0], 2))
-    layout = coerce_fa2_layout(layout)
     # actual drawing
     if layout == "fa":
         positions = np.array(fa2_positions(adjacency, init_coords, **kwds))
@@ -161,18 +166,40 @@ def draw_graph(  # noqa: PLR0913
             else:
                 ig_layout = g.layout(layout, **kwds)
         positions = np.array(ig_layout.coords)
-    adata.uns["draw_graph"] = {}
-    adata.uns["draw_graph"]["params"] = dict(layout=layout, **meta_random_state)
-    key_added = f"X_draw_graph_{key_added_ext or layout}"
-    adata.obsm[key_added] = positions
+    adata.uns[key_uns] = {}
+    adata.uns[key_uns]["params"] = dict(layout=layout, **meta_random_state)
+    adata.obsm[key_obsm] = positions
     logg.info(
         "    finished",
         time=start,
-        deep=f"added\n    {key_added!r}, graph_drawing coordinates (adata.obsm)",
+        deep="added"
+        f"\n    {key_obsm!r}, draw_graph coordinates (adata.obsm)"
+        f"\n    {key_uns!r}, draw_graph parameters (adata.uns)",
     )
     return adata if copy else None
 
 
+def _draw_graph_keys(
+    key_added: str | None | Default | Preset,
+    layout: str,
+    key_added_ext: str | None = None,
+) -> tuple[str, str]:
+    if key_added_ext is not None:
+        msg = "Passing `key_added_ext` is deprecated, use `key_added`’s template functionality instead."
+        warn(msg, category=FutureWarning)
+        suffix = key_added_ext
+    else:
+        suffix = layout
+    if isinstance(key_added, Default):
+        key_added = settings.preset
+    if isinstance(key_added, Preset):
+        key_added = key_added.draw_graph.key_added
+    if key_added is None:
+        return f"X_draw_graph_{suffix}", "draw_graph"
+    key_added = key_added.format(layout=suffix)
+    return key_added, key_added
+
+
 def fa2_positions(
     adjacency: CSBase | np.ndarray, init_coords: np.ndarray, **kwds
 ) -> list[tuple[float, float]]:
diff --git a/src/scanpy/tools/_embedding_density.py b/src/scanpy/tools/_embedding_density.py
index 37e2bcf606..ff823becb4 100644
--- a/src/scanpy/tools/_embedding_density.py
+++ b/src/scanpy/tools/_embedding_density.py
@@ -7,7 +7,7 @@
 import numpy as np
 
 from .. import logging as logg
-from .._utils import sanitize_anndata
+from .._utils import _get_basis_key, sanitize_anndata
 
 if TYPE_CHECKING:
     from collections.abc import Sequence
@@ -125,7 +125,7 @@ def embedding_density(  # noqa: PLR0912
     if basis == "fa":
         basis = "draw_graph_fa"
 
-    if f"X_{basis}" not in adata.obsm:
+    if _get_basis_key(adata, basis) is None:
         msg = (
             "Cannot find the embedded representation "
             f"`adata.obsm['X_{basis}']`. Compute the embedding first."
diff --git a/src/scanpy/tools/_ingest.py b/src/scanpy/tools/_ingest.py
index d85d6b89bb..f231093f1e 100644
--- a/src/scanpy/tools/_ingest.py
+++ b/src/scanpy/tools/_ingest.py
@@ -14,11 +14,14 @@
 from .._utils import (
     NeighborsView,
     _doc_params,
+    _existing_preset_keys,
     raise_not_implemented_error_if_backed_type,
 )
 from .._utils._doctests import doctest_skipif
 from .._utils.random import _legacy_random_state, _LegacyRng
 from ..neighbors import FlatTree
+from ..preprocessing._pca import _pca_keys
+from ..tools._umap import _umap_keys
 
 if TYPE_CHECKING:
     from collections.abc import Generator, Iterable
@@ -248,10 +251,10 @@ def _get_rng(self, params: dict[str, object]) -> np.random.Generator | None:
         random_state = params.get("random_state", 0)
         return _LegacyRng(random_state)
 
-    def _init_umap(self, adata: AnnData) -> None:
+    def _init_umap(self, adata: AnnData, obsm_key: str, uns_key: str) -> None:
         from umap import UMAP
 
-        rng = self._get_rng(adata.uns["umap"]["params"])
+        rng = self._get_rng(adata.uns[uns_key]["params"])
         self._umap = UMAP(
             metric=self._metric,
             random_state=_legacy_random_state(rng),
@@ -265,7 +268,7 @@ def _init_umap(self, adata: AnnData) -> None:
 
         self._umap._validate_parameters()
 
-        self._umap.embedding_ = adata.obsm["X_umap"]
+        self._umap.embedding_ = adata.obsm[obsm_key]
         self._umap._sparse_data = isinstance(self._rep, CSBase)
         self._umap._small_data = self._rep.shape[0] < 4096
         self._umap._metric_kwds = self._metric_kwds
@@ -275,8 +278,8 @@ def _init_umap(self, adata: AnnData) -> None:
 
         self._umap._knn_search_index = self._nnd_idx
 
-        self._umap._a = adata.uns["umap"]["params"]["a"]
-        self._umap._b = adata.uns["umap"]["params"]["b"]
+        self._umap._a = adata.uns[uns_key]["params"]["a"]
+        self._umap._b = adata.uns[uns_key]["params"]["b"]
 
         self._umap._input_hash = None
 
@@ -388,8 +391,8 @@ def __init__(
             )
             raise ValueError(msg)
 
-        if "X_umap" in adata.obsm:
-            self._init_umap(adata)
+        if keys := _existing_preset_keys(adata, _umap_keys):
+            self._init_umap(adata, *keys)
 
         self._obsm = None
         self._obs = None
@@ -554,10 +557,10 @@ def to_adata_joint(
                 self._obsm["rep"],
             ))
 
-        if "X_umap" in self._obsm:
-            adata.uns["umap"] = self._adata_ref.uns["umap"]
-        if "X_pca" in self._obsm:
-            adata.uns["pca"] = self._adata_ref.uns["pca"]
-            adata.varm["PCs"] = self._adata_ref.varm["PCs"]
+        if keys := _existing_preset_keys(self._adata_ref, _umap_keys):
+            adata.uns[keys[1]] = self._adata_ref.uns[keys[1]]
+        if keys := _existing_preset_keys(self._adata_ref, _pca_keys):
+            adata.varm[keys[1]] = self._adata_ref.varm[keys[1]]
+            adata.uns[keys[2]] = self._adata_ref.uns[keys[2]]
 
         return adata
diff --git a/src/scanpy/tools/_tsne.py b/src/scanpy/tools/_tsne.py
index 54fb28f436..81fcfe314e 100644
--- a/src/scanpy/tools/_tsne.py
+++ b/src/scanpy/tools/_tsne.py
@@ -5,7 +5,7 @@
 from .. import logging as logg
 from .._compat import warn
 from .._docs import doc_rng
-from .._settings import settings
+from .._settings import Default, Preset, settings
 from .._utils import _doc_params, raise_not_implemented_error_if_backed_type
 from .._utils.random import _accepts_legacy_random_state, _legacy_random_state
 from ..neighbors._doc import doc_n_pcs, doc_use_rep
@@ -17,6 +17,14 @@
     from .._utils.random import RNGLike, SeedLike
 
 
+def _tsne_keys(key_added: str | None | Default | Preset) -> tuple[str, str]:
+    if isinstance(key_added, Default):
+        key_added = settings.preset
+    if isinstance(key_added, Preset):
+        key_added = key_added.tsne.key_added
+    return ("X_tsne", "tsne") if key_added is None else (key_added, key_added)
+
+
 @_accepts_legacy_random_state(0)
 @_doc_params(doc_n_pcs=doc_n_pcs, use_rep=doc_use_rep, rng=doc_rng)
 def tsne(  # noqa: PLR0913
@@ -32,7 +40,7 @@ def tsne(  # noqa: PLR0913
     rng: SeedLike | RNGLike | None = None,
     use_fast_tsne: bool = False,
     n_jobs: int | None = None,
-    key_added: str | None = None,
+    key_added: str | None | Default = Default(preset=("tsne", "key_added")),
     copy: bool = False,
 ) -> AnnData | None:
     r"""t-SNE :cite:p:`vanDerMaaten2008,Amir2013,Pedregosa2011`.
@@ -102,6 +110,7 @@ def tsne(  # noqa: PLR0913
 
     """
     start = logg.info("computing tSNE")
+    key_obsm, key_uns = _tsne_keys(key_added)
     adata = adata.copy() if copy else adata
     x = _choose_representation(adata, use_rep=use_rep, n_pcs=n_pcs)
     raise_not_implemented_error_if_backed_type(x, "tsne")
@@ -157,7 +166,6 @@ def tsne(  # noqa: PLR0913
         use_rep=use_rep,
         n_components=n_components,
     )
-    key_uns, key_obsm = ("tsne", "X_tsne") if key_added is None else [key_added] * 2
     adata.obsm[key_obsm] = x_tsne  # annotate samples with tSNE coordinates
     adata.uns[key_uns] = dict(params={k: v for k, v in params.items() if v is not None})
 
diff --git a/src/scanpy/tools/_umap.py b/src/scanpy/tools/_umap.py
index 316c6c8aed..cd17ebd8be 100644
--- a/src/scanpy/tools/_umap.py
+++ b/src/scanpy/tools/_umap.py
@@ -7,7 +7,7 @@
 
 from .. import logging as logg
 from .._docs import doc_rng
-from .._settings import settings
+from .._settings import Default, Preset, settings
 from .._utils import NeighborsView, _doc_params
 from .._utils.random import (
     _accepts_legacy_random_state,
@@ -27,6 +27,16 @@
 type _InitPos = Literal["paga", "spectral", "random"]
 
 
+def _umap_keys(
+    key_added: str | None | Default | Preset = Default(),
+) -> tuple[str, str]:
+    if isinstance(key_added, Default):
+        key_added = settings.preset
+    if isinstance(key_added, Preset):
+        key_added = key_added.umap.key_added
+    return ("X_umap", "umap") if key_added is None else (key_added, key_added)
+
+
 @_accepts_legacy_random_state(0)
 @_doc_params(rng=doc_rng)
 def umap(  # noqa: PLR0913
@@ -44,7 +54,7 @@ def umap(  # noqa: PLR0913
     a: float | None = None,
     b: float | None = None,
     method: Literal["umap"] = "umap",
-    key_added: str | None = None,
+    key_added: str | None | Default = Default(preset=("umap", "key_added")),
     neighbors_key: str = "neighbors",
     copy: bool = False,
 ) -> AnnData | None:
@@ -144,7 +154,7 @@ def umap(  # noqa: PLR0913
     rng = np.random.default_rng(rng)
     adata = adata.copy() if copy else adata
 
-    key_obsm, key_uns = ("X_umap", "umap") if key_added is None else [key_added] * 2
+    key_obsm, key_uns = _umap_keys(key_added)
 
     if neighbors_key is None:  # backwards compat
         neighbors_key = "neighbors"
diff --git a/src/scanpy/tools/_utils.py b/src/scanpy/tools/_utils.py
index 80083a7023..b705cd0f3c 100644
--- a/src/scanpy/tools/_utils.py
+++ b/src/scanpy/tools/_utils.py
@@ -7,7 +7,7 @@
 from .. import logging as logg
 from .._compat import warn
 from .._settings import settings
-from .._utils import _choose_graph
+from .._utils import _choose_graph, _existing_preset_keys
 
 if TYPE_CHECKING:
     from anndata import AnnData
@@ -19,8 +19,8 @@
 def _choose_representation(
     adata: AnnData,
     *,
-    use_rep: str | None = None,
-    n_pcs: int | None = None,
+    use_rep: str | None,
+    n_pcs: int | None,
     silent: bool = False,
 ) -> np.ndarray | CSRBase:  # TODO: what else?
     verbosity = settings.verbosity
@@ -51,30 +51,30 @@ def _choose_representation(
 
 
 def _get_pca_or_small_x(adata: AnnData, n_pcs: int | None) -> np.ndarray | CSRBase:
+    from ..preprocessing._pca import _pca_keys, pca
+
     if adata.n_vars <= settings.N_PCS:
         logg.info("    using data matrix X directly")
         return adata.X
 
-    pca_key = next((k for k in ("pca", "X_pca") if k in adata.obsm), None)
-    if pca_key is not None:
+    if keys := _existing_preset_keys(adata, _pca_keys):
+        pca_key, *_ = keys
         if n_pcs is not None and n_pcs > adata.obsm[pca_key].shape[1]:
-            msg = f"`{pca_key}` does not have enough PCs. Rerun `sc.pp.pca` with adjusted `n_comps`."
+            msg = f"`adata.obsm[{pca_key!r}]` does not have enough PCs. Rerun `sc.pp.pca` with adjusted `n_comps`."
             raise ValueError(msg)
         x = adata.obsm[pca_key][:, :n_pcs]
         logg.info(f"    using {pca_key!r} with n_pcs = {x.shape[1]}")
         return x
 
-    from ..preprocessing import pca
-
     msg = (
         f"You’re trying to run this on {adata.n_vars} dimensions of `.X`, "
-        "if you really want this, set `use_rep='X'`.\n         "
+        "if you really want this, set `use_rep=’X’`.\n         "
         "Falling back to preprocessing with `sc.pp.pca` and default params."
     )
     warn(msg, UserWarning)
     n_pcs_pca = n_pcs if n_pcs is not None else settings.N_PCS
     pca(adata, n_comps=n_pcs_pca)
-    return adata.obsm[settings.preset.pca.key_added or "X_pca"]
+    return adata.obsm[_pca_keys()[0]]
 
 
 def get_init_pos_from_paga(
diff --git a/tests/test_embedding.py b/tests/test_embedding.py
index 436a72db0e..f1830aaedb 100644
--- a/tests/test_embedding.py
+++ b/tests/test_embedding.py
@@ -7,6 +7,7 @@
 from numpy.testing import assert_array_almost_equal, assert_array_equal, assert_raises
 
 import scanpy as sc
+from scanpy._settings import Default
 from testing.scanpy._helpers.data import pbmc68k_reduced
 from testing.scanpy._pytest.marks import needs
 
@@ -109,3 +110,54 @@ def test_diffmap(
         assert_array_equal(d1, d2)
     with subtests.test("different embedding"):
         assert_raises(AssertionError, assert_array_equal, d1, d3)
+
+
+@pytest.mark.parametrize(
+    ("key_added", "key_obsm", "key_uns"),
+    [
+        pytest.param(None, "X_diffmap", "diffmap_evals", id="None"),
+        pytest.param("custom_key", "custom_key", "custom_key", id="custom_key"),
+        pytest.param(sc.Preset.ScanpyV1, "X_diffmap", "diffmap_evals", id="v1"),
+        pytest.param(
+            *(sc.Preset.ScanpyV2Preview, "diffmap", "diffmap"),
+            marks=[needs.igraph, needs.skmisc],
+            id="v2",
+        ),
+    ],
+)
+def test_diffmap_key_added(
+    key_added: str | None | Default | sc.Preset, key_obsm: str, key_uns: str
+) -> None:
+    pbmc = pbmc68k_reduced()[:300, :100].copy()
+    if isinstance(key_added, sc.Preset):
+        sc.settings.preset = key_added
+        key_added = Default()
+    adata = sc.tl.diffmap(pbmc, key_added=key_added, copy=True)
+    assert key_obsm in adata.obsm
+    assert key_uns in adata.uns
+
+
+@needs.igraph
+@pytest.mark.parametrize(
+    ("key_added", "key_obsm", "key_uns"),
+    [
+        pytest.param(None, "X_draw_graph_fr", "draw_graph", id="None"),
+        pytest.param("custom_{layout}", "custom_fr", "custom_fr", id="custom_template"),
+        pytest.param(sc.Preset.ScanpyV1, "X_draw_graph_fr", "draw_graph", id="v1"),
+        pytest.param(
+            *(sc.Preset.ScanpyV2Preview, "graph_fr", "graph_fr"),
+            marks=needs.skmisc,
+            id="v2",
+        ),
+    ],
+)
+def test_draw_graph_key_added(
+    key_added: str | None | Default | sc.Preset, key_obsm: str, key_uns: str
+) -> None:
+    pbmc = pbmc68k_reduced()[:100, :100].copy()
+    if isinstance(key_added, sc.Preset):
+        sc.settings.preset = key_added
+        key_added = Default()
+    adata = sc.tl.draw_graph(pbmc, layout="fr", key_added=key_added, copy=True)
+    assert key_obsm in adata.obsm
+    assert key_uns in adata.uns
diff --git a/tests/test_sim.py b/tests/test_sim.py
index ac96966cb1..fb1fe9b8e7 100644
--- a/tests/test_sim.py
+++ b/tests/test_sim.py
@@ -6,9 +6,8 @@
 import scanpy as sc
 
 
+@pytest.mark.filterwarnings("ignore:.*Observation names are not unique:UserWarning")
 def test_sim_toggleswitch() -> None:
-    with pytest.warns(UserWarning, match=r"Observation names are not unique"):
-        adata_sim = sc.tl.sim("toggleswitch")
-    with pytest.warns(UserWarning, match=r"Observation names are not unique"):
-        adata_ds = sc.datasets.toggleswitch()
+    adata_sim = sc.tl.sim("toggleswitch")
+    adata_ds = sc.datasets.toggleswitch()
     np.allclose(adata_sim.X, adata_ds.X, np.finfo(np.float32).eps)