diff --git a/python/cudf/cudf/core/multiindex.py b/python/cudf/cudf/core/multiindex.py
index a82735be901..e6cee7c1038 100644
--- a/python/cudf/cudf/core/multiindex.py
+++ b/python/cudf/cudf/core/multiindex.py
@@ -190,6 +190,18 @@ def names(self):
     def names(self, value):
         value = [None] * self.nlevels if value is None else value
         assert len(value) == self.nlevels
+
+        if len(value) == len(set(value)):
+            # IMPORTANT: if the provided names are unique,
+            # we reconstruct self._data with the names as keys.
+            # If they are not unique, the keys of self._data
+            # and self._names will be different, which can lead
+            # to unexpected behaviour in some cases. This is
+            # definitely buggy, but we can't disallow non-unique
+            # names either...
+            self._data = self._data._create_unsafe(
+                dict(zip(value, self._data.values()))
+            )
         self._names = pd.core.indexes.frozen.FrozenList(value)
 
     def rename(self, names, inplace=False):
diff --git a/python/cudf/cudf/tests/test_joining.py b/python/cudf/cudf/tests/test_joining.py
index 50141428b02..9164bfe98d1 100644
--- a/python/cudf/cudf/tests/test_joining.py
+++ b/python/cudf/cudf/tests/test_joining.py
@@ -1725,3 +1725,16 @@ def test_merge_with_lists(how):
     got = gd_left.merge(gd_right, on="a")
 
     assert_join_results_equal(expect, got, how=how)
+
+
+def test_join_renamed_index():
+    df = cudf.DataFrame(
+        {0: [1, 2, 3, 4, 5], 1: [1, 2, 3, 4, 5], "c": [1, 2, 3, 4, 5]}
+    ).set_index([0, 1])
+    df.index.names = ["a", "b"]  # doesn't actually change df._index._data
+
+    expect = df.to_pandas().merge(
+        df.to_pandas(), left_index=True, right_index=True
+    )
+    got = df.merge(df, left_index=True, right_index=True, how="inner")
+    assert_join_results_equal(expect, got, how="inner")