diff --git a/pandas/core/groupby/generic.py b/pandas/core/groupby/generic.py
index 35cb247e96bc3..8bb8f00b4c406 100644
--- a/pandas/core/groupby/generic.py
+++ b/pandas/core/groupby/generic.py
@@ -354,35 +354,17 @@ def array_func(values: ArrayLike) -> ArrayLike:
         )
         return self._reindex_output(ser)
 
-    def _wrap_aggregated_output(
-        self,
-        output: Mapping[base.OutputKey, Series | ArrayLike],
+    def _indexed_output_to_ndframe(
+        self, output: Mapping[base.OutputKey, ArrayLike]
     ) -> Series:
         """
-        Wraps the output of a SeriesGroupBy aggregation into the expected result.
-
-        Parameters
-        ----------
-        output : Mapping[base.OutputKey, Union[Series, ArrayLike]]
-            Data to wrap.
-
-        Returns
-        -------
-        Series
-
-        Notes
-        -----
-        In the vast majority of cases output will only contain one element.
-        The exception is operations that expand dimensions, like ohlc.
+        Wrap the dict result of a GroupBy aggregation into a Series.
         """
         assert len(output) == 1
-
-        name = self.obj.name
-        index = self.grouper.result_index
         values = next(iter(output.values()))
-
-        result = self.obj._constructor(values, index=index, name=name)
-        return self._reindex_output(result)
+        result = self.obj._constructor(values)
+        result.name = self.obj.name
+        return result
 
     def _wrap_transformed_output(
         self, output: Mapping[base.OutputKey, Series | ArrayLike]
@@ -1614,46 +1596,19 @@ def _insert_inaxis_grouper_inplace(self, result: DataFrame) -> None:
             if in_axis and name not in columns:
                 result.insert(0, name, lev)
 
-    def _wrap_aggregated_output(
-        self,
-        output: Mapping[base.OutputKey, Series | ArrayLike],
+    def _indexed_output_to_ndframe(
+        self, output: Mapping[base.OutputKey, ArrayLike]
     ) -> DataFrame:
         """
-        Wraps the output of DataFrameGroupBy aggregations into the expected result.
-
-        Parameters
-        ----------
-        output : Mapping[base.OutputKey, Union[Series, np.ndarray]]
-           Data to wrap.
-
-        Returns
-        -------
-        DataFrame
+        Wrap the dict result of a GroupBy aggregation into a DataFrame.
         """
-        if isinstance(output, DataFrame):
-            result = output
-        else:
-            indexed_output = {key.position: val for key, val in output.items()}
-            columns = Index([key.label for key in output])
-            columns._set_names(self._obj_with_exclusions._get_axis(1 - self.axis).names)
-
-            result = self.obj._constructor(indexed_output)
-            result.columns = columns
-
-        if not self.as_index:
-            self._insert_inaxis_grouper_inplace(result)
-            result = result._consolidate()
-        else:
-            result.index = self.grouper.result_index
-
-        if self.axis == 1:
-            result = result.T
-            if result.index.equals(self.obj.index):
-                # Retain e.g. DatetimeIndex/TimedeltaIndex freq
-                result.index = self.obj.index.copy()
-                # TODO: Do this more systematically
+        indexed_output = {key.position: val for key, val in output.items()}
+        columns = Index([key.label for key in output])
+        columns._set_names(self._obj_with_exclusions._get_axis(1 - self.axis).names)
 
-        return self._reindex_output(result)
+        result = self.obj._constructor(indexed_output)
+        result.columns = columns
+        return result
 
     def _wrap_transformed_output(
         self, output: Mapping[base.OutputKey, Series | ArrayLike]
diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index 0e358e611f418..a60ec29581337 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -1095,9 +1095,54 @@ def _set_result_index_ordered(
 
         return result
 
-    def _wrap_aggregated_output(self, output: Mapping[base.OutputKey, ArrayLike]):
+    def _indexed_output_to_ndframe(
+        self, result: Mapping[base.OutputKey, ArrayLike]
+    ) -> Series | DataFrame:
         raise AbstractMethodError(self)
 
+    def _wrap_aggregated_output(
+        self, output: Series | DataFrame | Mapping[base.OutputKey, ArrayLike]
+    ):
+        """
+        Wraps the output of GroupBy aggregations into the expected result.
+
+        Parameters
+        ----------
+        output : Series, DataFrame, or Mapping[base.OutputKey, ArrayLike]
+           Data to wrap.
+
+        Returns
+        -------
+        Series or DataFrame
+        """
+
+        if isinstance(output, (Series, DataFrame)):
+            # We get here (for DataFrameGroupBy) if we used Manager.grouped_reduce,
+            #  in which case our columns are already set correctly.
+            # ATM we do not get here for SeriesGroupBy; when we do, we will
+            #  need to require that result.name already match self.obj.name
+            result = output
+        else:
+            result = self._indexed_output_to_ndframe(output)
+
+        if not self.as_index:
+            # `not self.as_index` is only relevant for DataFrameGroupBy,
+            #   enforced in __init__
+            self._insert_inaxis_grouper_inplace(result)
+            result = result._consolidate()
+        else:
+            result.index = self.grouper.result_index
+
+        if self.axis == 1:
+            # Only relevant for DataFrameGroupBy, no-op for SeriesGroupBy
+            result = result.T
+            if result.index.equals(self.obj.index):
+                # Retain e.g. DatetimeIndex/TimedeltaIndex freq
+                result.index = self.obj.index.copy()
+                # TODO: Do this more systematically
+
+        return self._reindex_output(result)
+
     def _wrap_transformed_output(self, output: Mapping[base.OutputKey, ArrayLike]):
         raise AbstractMethodError(self)