diff --git a/doc/whats_new/v1.4.rst b/doc/whats_new/v1.4.rst
index 613e791b7bb78..38f7a33ab9651 100644
--- a/doc/whats_new/v1.4.rst
+++ b/doc/whats_new/v1.4.rst
@@ -255,6 +255,10 @@ Changelog
   which returns a dense numpy ndarray as before.
   :pr:`27438` by :user:`Yao Xiao <Charlie-XIAO>`.
 
+- |API| :func:`datasets.make_sparse_spd_matrix` deprecated the keyword argument ``dim``
+  in favor of ``n_dim``. ``dim`` will be removed in version 1.6.
+  :pr:`27718` by :user:`Adam Li <adam2392>`.
+
 :mod:`sklearn.decomposition`
 ............................
 
diff --git a/sklearn/datasets/_samples_generator.py b/sklearn/datasets/_samples_generator.py
index 828b44e8c7859..cd0bb4b3dbba8 100644
--- a/sklearn/datasets/_samples_generator.py
+++ b/sklearn/datasets/_samples_generator.py
@@ -1571,7 +1571,7 @@ def make_spd_matrix(n_dim, *, random_state=None):
 
 @validate_params(
     {
-        "dim": [Interval(Integral, 1, None, closed="left")],
+        "n_dim": [Hidden(None), Interval(Integral, 1, None, closed="left")],
         "alpha": [Interval(Real, 0, 1, closed="both")],
         "norm_diag": ["boolean"],
         "smallest_coef": [Interval(Real, 0, 1, closed="both")],
@@ -1581,11 +1581,15 @@ def make_spd_matrix(n_dim, *, random_state=None):
             None,
         ],
         "random_state": ["random_state"],
+        "dim": [
+            Interval(Integral, 1, None, closed="left"),
+            Hidden(StrOptions({"deprecated"})),
+        ],
     },
     prefer_skip_nested_validation=True,
 )
 def make_sparse_spd_matrix(
-    dim=1,
+    n_dim=None,
     *,
     alpha=0.95,
     norm_diag=False,
@@ -1593,6 +1597,7 @@ def make_sparse_spd_matrix(
     largest_coef=0.9,
     sparse_format=None,
     random_state=None,
+    dim="deprecated",
 ):
     """Generate a sparse symmetric definite positive matrix.
 
@@ -1600,9 +1605,12 @@ def make_sparse_spd_matrix(
 
     Parameters
     ----------
-    dim : int, default=1
+    n_dim : int, default=1
         The size of the random matrix to generate.
 
+        .. versionchanged:: 1.4
+            Renamed from ``dim`` to ``n_dim``.
+
     alpha : float, default=0.95
         The probability that a coefficient is zero (see notes). Larger values
         enforce more sparsity. The value should be in the range 0 and 1.
@@ -1628,6 +1636,12 @@ def make_sparse_spd_matrix(
         for reproducible output across multiple function calls.
         See :term:`Glossary <random_state>`.
 
+    dim : int, default=1
+        The size of the random matrix to generate.
+
+        .. deprecated:: 1.4
+            `dim` is deprecated and will be removed in 1.6.
+
     Returns
     -------
     prec : ndarray or sparse matrix of shape (dim, dim)
@@ -1646,10 +1660,32 @@ def make_sparse_spd_matrix(
     """
     random_state = check_random_state(random_state)
 
-    chol = -sp.eye(dim)
+    # TODO(1.6): remove in 1.6
+    # Also make sure to change `n_dim` default back to 1 and deprecate None
+    if n_dim is not None and dim != "deprecated":
+        raise ValueError(
+            "`dim` and `n_dim` cannot be both specified. Please use `n_dim` only "
+            "as `dim` is deprecated in v1.4 and will be removed in v1.6."
+        )
+
+    if dim != "deprecated":
+        warnings.warn(
+            (
+                "dim was deprecated in version 1.4 and will be removed in 1.6."
+                "Please use ``n_dim`` instead."
+            ),
+            FutureWarning,
+        )
+        _n_dim = dim
+    elif n_dim is None:
+        _n_dim = 1
+    else:
+        _n_dim = n_dim
+
+    chol = -sp.eye(_n_dim)
     aux = sp.random(
-        m=dim,
-        n=dim,
+        m=_n_dim,
+        n=_n_dim,
         density=1 - alpha,
         data_rvs=lambda x: random_state.uniform(
             low=smallest_coef, high=largest_coef, size=x
@@ -1661,7 +1697,7 @@ def make_sparse_spd_matrix(
 
     # Permute the lines: we don't want to have asymmetries in the final
     # SPD matrix
-    permutation = random_state.permutation(dim)
+    permutation = random_state.permutation(_n_dim)
     aux = aux[permutation].T[permutation]
     chol += aux
     prec = chol.T @ chol
diff --git a/sklearn/datasets/tests/test_samples_generator.py b/sklearn/datasets/tests/test_samples_generator.py
index 82637cbaa90df..6c5d822163e63 100644
--- a/sklearn/datasets/tests/test_samples_generator.py
+++ b/sklearn/datasets/tests/test_samples_generator.py
@@ -559,15 +559,15 @@ def test_make_spd_matrix():
     "sparse_format", [None, "bsr", "coo", "csc", "csr", "dia", "dok", "lil"]
 )
 def test_make_sparse_spd_matrix(norm_diag, sparse_format, global_random_seed):
-    dim = 5
+    n_dim = 5
     X = make_sparse_spd_matrix(
-        dim=dim,
+        n_dim=n_dim,
         norm_diag=norm_diag,
         sparse_format=sparse_format,
         random_state=global_random_seed,
     )
 
-    assert X.shape == (dim, dim), "X shape mismatch"
+    assert X.shape == (n_dim, n_dim), "X shape mismatch"
     if sparse_format is None:
         assert not sp.issparse(X)
         assert_allclose(X, X.T)
@@ -585,7 +585,27 @@ def test_make_sparse_spd_matrix(norm_diag, sparse_format, global_random_seed):
 
     if norm_diag:
         # Check that leading diagonal elements are 1
-        assert_array_almost_equal(Xarr.diagonal(), np.ones(dim))
+        assert_array_almost_equal(Xarr.diagonal(), np.ones(n_dim))
+
+
+# TODO(1.6): remove
+def test_make_sparse_spd_matrix_deprecation_warning():
+    """Check the message for future deprecation."""
+    warn_msg = "dim was deprecated in version 1.4"
+    with pytest.warns(FutureWarning, match=warn_msg):
+        make_sparse_spd_matrix(
+            dim=1,
+        )
+
+    error_msg = "`dim` and `n_dim` cannot be both specified"
+    with pytest.raises(ValueError, match=error_msg):
+        make_sparse_spd_matrix(
+            dim=1,
+            n_dim=1,
+        )
+
+    X = make_sparse_spd_matrix()
+    assert X.shape[1] == 1
 
 
 @pytest.mark.parametrize("hole", [False, True])