BUG: fix empty groupby(..., as_index=False).apply(...) index name inconsistency (#65332)

Author: Ashish-ml-eng

doc/source/whatsnew/v3.1.0.rst

@@ -340,6 +340,7 @@ Groupby/resample/rolling
 ^^^^^^^^^^^^^^^^^^^^^^^^
 - Bug in :meth:`.DataFrameGroupBy.agg` when there are no groups, multiple keys, and ``group_keys=False`` (:issue:`51445`)
 - Bug in :meth:`.DataFrameGroupBy.agg` would operate on the group as a whole when ``args`` or ``kwargs`` are supplied for the provided ``func``; now this method only operates on each Series of the group (:issue:`39169`)
+- Bug in :meth:`.DataFrameGroupBy.apply` with ``as_index=False`` where applying on an empty :class:`DataFrame` returned inconsistent index metadata compared to non-empty results (:issue:`48135`)
 - Bug in :meth:`.GroupBy.any` and :meth:`.GroupBy.all` returning ``NaN`` with ``float64`` dtype for unobserved categorical groups on NumPy ``bool`` data instead of the boolean identity value with ``bool`` dtype (:issue:`65100`)
 - Bug in :meth:`.Rolling.skew` and :meth:`.Rolling.kurt` (and their :class:`GroupBy` counterparts) returning ``0.0`` and ``-3.0`` respectively for degenerate windows or groups; these now return ``NaN`` (:issue:`62864`)
 - Bug in :meth:`.Rolling.skew` and :meth:`.Rolling.kurt` returning ``NaN`` for low-variance windows (:issue:`62946`)

pandas/core/groupby/generic.py

@@ -2393,7 +2393,7 @@ def _wrap_applied_output(
             if is_transform:
                 # GH#47787 see test_group_on_empty_multiindex
                 res_index = data.index
-            elif not self.group_keys:
+            elif not self.group_keys or not self.as_index:
                 res_index = None
             else:
                 res_index = self._grouper.result_index

pandas/tests/groupby/test_apply.py

@@ -1541,3 +1541,29 @@ def addstore(x):
 
     tm.assert_frame_equal(store[0], expected_out_0)
     tm.assert_frame_equal(store[1], expected_out_1)
+
+
+@pytest.mark.parametrize("test_empty", [False, True])
+def test_apply_as_index_false_empty_index_name(test_empty):
+    # https://github.com/pandas-dev/pandas/issues/48135
+    df = DataFrame({"A": [4, 4, 4], "B": [9, 9, 9]})
+
+    if test_empty:
+        df = df.iloc[:0]
+
+    gb = df.groupby("A", as_index=False)
+    result = gb.apply(lambda x: x)
+
+    if test_empty:
+        expected = DataFrame(
+            {"B": Series([], dtype="int64")},
+            index=Index([], dtype="int64"),
+        )
+    else:
+        expected = DataFrame(
+            {"B": [9, 9, 9]},
+            index=Index([0, 1, 2], dtype="int64"),
+        )
+
+    expected.index.name = None
+    tm.assert_frame_equal(result, expected)