BUG: assign consensus name to index union in array case GH13475

Author: iamlemec

pandas/core/indexes/api.py

@@ -218,9 +218,8 @@ def conv(i):
             return result
     elif kind == "array":
         index = indexes[0]
-        for other in indexes[1:]:
-            if not index.equals(other):
-                return _unique_indices(indexes)
+        if not all(index.equals(other) for other in indexes[1:]):
+            index = _unique_indices(indexes)
 
         name = get_consensus_names(indexes)[0]
         if name != index.name:

pandas/tests/reshape/test_concat.py

@@ -1279,6 +1279,33 @@ def test_concat_ignore_index(self, sort):
 
         tm.assert_frame_equal(v1, expected)
 
+    @pytest.mark.parametrize(
+        "input_names,output_name",
+        [
+            (["idx", "idx"], "idx"),
+            (["idx", None], "idx"),
+            ([None, None], None),
+            (["idx1", "idx2"], None),
+            (["idx", "idx", None], "idx"),
+            (["idx1", "idx2", None], None),
+        ],
+    )
+    def test_concat_same_index_names(self, input_names, output_name):
+        # GH13475
+        indices = [pd.Index(["a", "b", "c"], name=n) for n in input_names]
+        frames = [
+            pd.DataFrame({c: [0, 1, 2]}, index=i)
+            for i, c in zip(indices, ["x", "y", "z"])
+        ]
+        result = pd.concat(frames, axis=1)
+
+        exp_ind = pd.Index(["a", "b", "c"], name=output_name)
+        expected = pd.DataFrame(
+            {c: [0, 1, 2] for _, c in zip(input_names, ["x", "y", "z"])}, index=exp_ind
+        )
+
+        tm.assert_frame_equal(result, expected)
+
     def test_concat_multiindex_with_keys(self):
         index = MultiIndex(
             levels=[["foo", "bar", "baz", "qux"], ["one", "two", "three"]],