BUG-46369: add test

Author: ma3da

pandas/tests/groupby/test_apply.py

@@ -1317,3 +1317,14 @@ def test_apply_str_with_args(df, args, kwargs):
     result = gb.apply("sum", *args, **kwargs)
     expected = gb.sum(numeric_only=True)
     tm.assert_frame_equal(result, expected)
+
+
+def test_name_one_group():
+    # GH 46369
+    df = DataFrame({"a": [0], "b": [1]})
+    ser = df["b"].rename(None)
+
+    result = ser.groupby(df["a"]).apply(lambda x: x).name
+    expected = None
+
+    assert result is expected