diff --git a/doc/source/whatsnew/v2.1.0.rst b/doc/source/whatsnew/v2.1.0.rst
index 743bb78c70c36..845fa5dfde428 100644
--- a/doc/source/whatsnew/v2.1.0.rst
+++ b/doc/source/whatsnew/v2.1.0.rst
@@ -295,6 +295,7 @@ Groupby/resample/rolling
   or :class:`PeriodIndex`, and the ``groupby`` method was given a function as its first argument,
   the function operated on the whole index rather than each element of the index. (:issue:`51979`)
 - Bug in :meth:`GroupBy.var` failing to raise ``TypeError`` when called with datetime64 or :class:`PeriodDtype` values (:issue:`52128`)
+- Bug in :meth:`DataFrameGroupBy.apply` causing an error to be raised when the input :class:`DataFrame` was subset as a :class:`DataFrame` after groupby (``[['a']]`` and not ``['a']``) and the given callable returned :class:`Series` that were not all indexed the same. (:issue:`52444`)
 -
 
 Reshaping
diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index b832eb90aa422..7f2eccbf8b2d1 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -1192,7 +1192,13 @@ def _concat_objects(
         else:
             result = concat(values, axis=self.axis)
 
-        name = self.obj.name if self.obj.ndim == 1 else self._selection
+        if self.obj.ndim == 1:
+            name = self.obj.name
+        elif is_hashable(self._selection):
+            name = self._selection
+        else:
+            name = None
+
         if isinstance(result, Series) and name is not None:
             result.name = name
 
diff --git a/pandas/tests/groupby/test_apply.py b/pandas/tests/groupby/test_apply.py
index 0699b7c1369f2..b56ce326d1962 100644
--- a/pandas/tests/groupby/test_apply.py
+++ b/pandas/tests/groupby/test_apply.py
@@ -1203,6 +1203,26 @@ def test_groupby_apply_shape_cache_safety():
     tm.assert_frame_equal(result, expected)
 
 
+def test_groupby_apply_to_series_name():
+    # GH52444
+    df = DataFrame.from_dict(
+        {
+            "a": ["a", "b", "a", "b"],
+            "b1": ["aa", "ac", "ac", "ad"],
+            "b2": ["aa", "aa", "aa", "ac"],
+        }
+    )
+    grp = df.groupby("a")[["b1", "b2"]]
+    result = grp.apply(lambda x: x.unstack().value_counts())
+
+    expected_idx = MultiIndex.from_arrays(
+        arrays=[["a", "a", "b", "b", "b"], ["aa", "ac", "ac", "ad", "aa"]],
+        names=["a", None],
+    )
+    expected = Series([3, 1, 2, 1, 1], index=expected_idx, name="count")
+    tm.assert_series_equal(result, expected)
+
+
 @pytest.mark.parametrize("dropna", [True, False])
 def test_apply_na(dropna):
     # GH#28984