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diff --git a/‎doc/whats_new/v1.3.rst
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diff --git a/‎sklearn/preprocessing/_encoders.py
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diff --git a/‎sklearn/preprocessing/tests/test_encoders.py
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@@ -144,6 +144,13 @@ Changelog
 
 :mod:`sklearn.preprocessing`
 ............................
+
+- |Enhancement| Adds a `feature_name_combiner` parameter to
+  :class:`preprocessing.OneHotEncoder`. This specifies a custom callable to create
+  feature names to be returned by :meth:`get_feature_names_out`.
+  The callable combines input arguments `(input_feature, category)` to a string.
+  :pr:`22506` by :user:`Mario Kostelac <mariokostelac>`.
+
 - |Enhancement| Added support for `sample_weight` in
   :class:`preprocessing.KBinsDiscretizer`. This allows specifying the parameter
   `sample_weight` for each sample to be used while fitting. The option is only
 
@@ -343,6 +343,17 @@ class OneHotEncoder(_BaseEncoder):
         .. versionadded:: 1.1
             Read more in the :ref:`User Guide <one_hot_encoder_infrequent_categories>`.
 
+    feature_name_combiner : "concat" or callable, default="concat"
+        Callable with signature `def callable(input_feature, category)` that returns a
+        string. This is used to create feature names to be returned by
+        :meth:`get_feature_names_out`.
+
+        `"concat"` concatenates encoded feature name and category with
+        `feature + "_" + str(category)`.E.g. feature X with values 1, 6, 7 create
+        feature names `X_1, X_6, X_7`.
+
+        .. versionadded:: 1.3
+
     Attributes
     ----------
     categories_ : list of arrays
@@ -388,6 +399,13 @@ class OneHotEncoder(_BaseEncoder):
 
         .. versionadded:: 1.0
 
+    feature_name_combiner : callable or None
+        Callable with signature `def callable(input_feature, category)` that returns a
+        string. This is used to create feature names to be returned by
+        :meth:`get_feature_names_out`.
+
+        .. versionadded:: 1.3
+
     See Also
     --------
     OrdinalEncoder : Performs an ordinal (integer)
@@ -442,6 +460,15 @@ class OneHotEncoder(_BaseEncoder):
     array([[0., 1., 0., 0.],
            [1., 0., 1., 0.]])
 
+    One can change the way feature names are created.
+
+    >>> def custom_combiner(feature, category):
+    ...     return str(feature) + "_" + type(category).__name__ + "_" + str(category)
+    >>> custom_fnames_enc = OneHotEncoder(feature_name_combiner=custom_combiner).fit(X)
+    >>> custom_fnames_enc.get_feature_names_out()
+    array(['x0_str_Female', 'x0_str_Male', 'x1_int_1', 'x1_int_2', 'x1_int_3'],
+          dtype=object)
+
     Infrequent categories are enabled by setting `max_categories` or `min_frequency`.
 
     >>> import numpy as np
@@ -467,6 +494,7 @@ class OneHotEncoder(_BaseEncoder):
         ],
         "sparse": [Hidden(StrOptions({"deprecated"})), "boolean"],  # deprecated
         "sparse_output": ["boolean"],
+        "feature_name_combiner": [StrOptions({"concat"}), callable],
     }
 
     def __init__(
@@ -480,6 +508,7 @@ def __init__(
         handle_unknown="error",
         min_frequency=None,
         max_categories=None,
+        feature_name_combiner="concat",
     ):
         self.categories = categories
         # TODO(1.4): Remove self.sparse
@@ -490,6 +519,7 @@ def __init__(
         self.drop = drop
         self.min_frequency = min_frequency
         self.max_categories = max_categories
+        self.feature_name_combiner = feature_name_combiner
 
     @property
     def infrequent_categories_(self):
@@ -1060,13 +1090,26 @@ def get_feature_names_out(self, input_features=None):
             for i, _ in enumerate(self.categories_)
         ]
 
+        name_combiner = self._check_get_feature_name_combiner()
         feature_names = []
         for i in range(len(cats)):
-            names = [input_features[i] + "_" + str(t) for t in cats[i]]
+            names = [name_combiner(input_features[i], t) for t in cats[i]]
             feature_names.extend(names)
 
         return np.array(feature_names, dtype=object)
 
+    def _check_get_feature_name_combiner(self):
+        if self.feature_name_combiner == "concat":
+            return lambda feature, category: feature + "_" + str(category)
+        else:  # callable
+            dry_run_combiner = self.feature_name_combiner("feature", "category")
+            if not isinstance(dry_run_combiner, str):
+                raise TypeError(
+                    "When `feature_name_combiner` is a callable, it should return a "
+                    f"Python string. Got {type(dry_run_combiner)} instead."
+                )
+            return self.feature_name_combiner
+
 
 class OrdinalEncoder(OneToOneFeatureMixin, _BaseEncoder):
     """
 
@@ -193,6 +193,32 @@ def test_one_hot_encoder_feature_names_unicode():
     assert_array_equal(["n👍me_c❤t1", "n👍me_dat2"], feature_names)
 
 
+def test_one_hot_encoder_custom_feature_name_combiner():
+    """Check the behaviour of `feature_name_combiner` as a callable."""
+
+    def name_combiner(feature, category):
+        return feature + "_" + repr(category)
+
+    enc = OneHotEncoder(feature_name_combiner=name_combiner)
+    X = np.array([["None", None]], dtype=object).T
+    enc.fit(X)
+    feature_names = enc.get_feature_names_out()
+    assert_array_equal(["x0_'None'", "x0_None"], feature_names)
+    feature_names = enc.get_feature_names_out(input_features=["a"])
+    assert_array_equal(["a_'None'", "a_None"], feature_names)
+
+    def wrong_combiner(feature, category):
+        # we should be returning a Python string
+        return 0
+
+    enc = OneHotEncoder(feature_name_combiner=wrong_combiner).fit(X)
+    err_msg = (
+        "When `feature_name_combiner` is a callable, it should return a Python string."
+    )
+    with pytest.raises(TypeError, match=err_msg):
+        enc.get_feature_names_out()
+
+
 def test_one_hot_encoder_set_params():
     X = np.array([[1, 2]]).T
     oh = OneHotEncoder()