diff --git a/python/cudf/cudf/core/reshape.py b/python/cudf/cudf/core/reshape.py
index edcc4ab3e63..160c88f0684 100644
--- a/python/cudf/cudf/core/reshape.py
+++ b/python/cudf/cudf/core/reshape.py
@@ -438,13 +438,16 @@ def concat(objs, axis=0, join="outer", ignore_index=False, sort=None):
                     else:
                         df[col_label] = col
 
-        if ignore_index:
-            # with ignore_index the column names change to numbers
-            df.columns = pd.RangeIndex(len(result_columns))
-        elif not only_series:
-            df.columns = cudf.MultiIndex.from_tuples(df._column_names)
+        if keys is None:
+            df.columns = result_columns.unique()
+            if ignore_index:
+                df.columns = pd.RangeIndex(len(result_columns.unique()))
         else:
-            pass
+            if ignore_index:
+                # with ignore_index the column names change to numbers
+                df.columns = pd.RangeIndex(len(result_columns))
+            elif not only_series:
+                df.columns = cudf.MultiIndex.from_tuples(df._column_names)
 
         if empty_inner:
             # if join is inner and it contains an empty df
diff --git a/python/cudf/cudf/tests/test_concat.py b/python/cudf/cudf/tests/test_concat.py
index ede8c620d2d..e4c6ab7daa4 100644
--- a/python/cudf/cudf/tests/test_concat.py
+++ b/python/cudf/cudf/tests/test_concat.py
@@ -218,7 +218,8 @@ def test_concat_columns(axis):
     assert_eq(expect, got, check_index_type=True)
 
 
-def test_concat_multiindex_dataframe():
+@pytest.mark.parametrize("axis", [0, 1])
+def test_concat_multiindex_dataframe(axis):
     gdf = cudf.DataFrame(
         {
             "w": np.arange(4),
@@ -233,14 +234,11 @@ def test_concat_multiindex_dataframe():
     pdg2 = pdg.iloc[:, 1:]
     gdg1 = cudf.from_pandas(pdg1)
     gdg2 = cudf.from_pandas(pdg2)
+    expected = pd.concat([pdg1, pdg2], axis=axis)
+    result = cudf.concat([gdg1, gdg2], axis=axis)
     assert_eq(
-        cudf.concat([gdg1, gdg2]).astype("float64"),
-        pd.concat([pdg1, pdg2]),
-        check_index_type=True,
-    )
-    assert_eq(
-        cudf.concat([gdg1, gdg2], axis=1),
-        pd.concat([pdg1, pdg2], axis=1),
+        expected,
+        result,
         check_index_type=True,
     )