diff --git a/doc/source/whatsnew/v1.5.0.rst b/doc/source/whatsnew/v1.5.0.rst
index 98d56bac402ac..97ff3a9af6e26 100644
--- a/doc/source/whatsnew/v1.5.0.rst
+++ b/doc/source/whatsnew/v1.5.0.rst
@@ -602,6 +602,7 @@ Groupby/resample/rolling
 - Bug in :meth:`GroupBy.cummax` with ``int64`` dtype with leading value being the smallest possible int64 (:issue:`46382`)
 - Bug in :meth:`GroupBy.max` with empty groups and ``uint64`` dtype incorrectly raising ``RuntimeError`` (:issue:`46408`)
 - Bug in :meth:`.GroupBy.apply` would fail when ``func`` was a string and args or kwargs were supplied (:issue:`46479`)
+- Bug in :meth:`SeriesGroupBy.apply` would incorrectly name its result when there was a unique group (:issue:`46369`)
 - Bug in :meth:`.Rolling.var` would segfault calculating weighted variance when window size was larger than data size (:issue:`46760`)
 
 Reshaping
diff --git a/pandas/core/common.py b/pandas/core/common.py
index 6c3d2c91ab012..90f665362ef56 100644
--- a/pandas/core/common.py
+++ b/pandas/core/common.py
@@ -612,7 +612,7 @@ def get_cython_func(arg: Callable) -> str | None:
 
 def is_builtin_func(arg):
     """
-    if we define an builtin function for this argument, return it,
+    if we define a builtin function for this argument, return it,
     otherwise return the arg
     """
     return _builtin_table.get(arg, arg)
diff --git a/pandas/core/groupby/generic.py b/pandas/core/groupby/generic.py
index 8d9b94f242e33..06a1aed8e3b09 100644
--- a/pandas/core/groupby/generic.py
+++ b/pandas/core/groupby/generic.py
@@ -397,11 +397,13 @@ def _wrap_applied_output(
             res_ser.name = self.obj.name
             return res_ser
         elif isinstance(values[0], (Series, DataFrame)):
-            return self._concat_objects(
+            result = self._concat_objects(
                 values,
                 not_indexed_same=not_indexed_same,
                 override_group_keys=override_group_keys,
             )
+            result.name = self.obj.name
+            return result
         else:
             # GH #6265 #24880
             result = self.obj._constructor(
diff --git a/pandas/tests/groupby/test_apply.py b/pandas/tests/groupby/test_apply.py
index 9cb64766a1079..4cfc3ea41543b 100644
--- a/pandas/tests/groupby/test_apply.py
+++ b/pandas/tests/groupby/test_apply.py
@@ -1320,3 +1320,13 @@ 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)
+
+
+@pytest.mark.parametrize("name", ["some_name", None])
+def test_result_name_when_one_group(name):
+    # GH 46369
+    ser = Series([1, 2], name=name)
+    result = ser.groupby(["a", "a"], group_keys=False).apply(lambda x: x)
+    expected = Series([1, 2], name=name)
+
+    tm.assert_series_equal(result, expected)
diff --git a/pandas/tests/groupby/test_value_counts.py b/pandas/tests/groupby/test_value_counts.py
index d38ba84cd1397..577a72d3f5090 100644
--- a/pandas/tests/groupby/test_value_counts.py
+++ b/pandas/tests/groupby/test_value_counts.py
@@ -183,12 +183,11 @@ def test_series_groupby_value_counts_on_categorical():
                 ),
             ]
         ),
-        name=0,
     )
 
     # Expected:
     # 0  a    1
     #    b    0
-    # Name: 0, dtype: int64
+    # dtype: int64
 
     tm.assert_series_equal(result, expected)
diff --git a/pandas/tests/groupby/transform/test_transform.py b/pandas/tests/groupby/transform/test_transform.py
index a77c95e30ab43..237d6a96f39ec 100644
--- a/pandas/tests/groupby/transform/test_transform.py
+++ b/pandas/tests/groupby/transform/test_transform.py
@@ -1511,10 +1511,5 @@ def test_null_group_str_transformer_series(request, dropna, transformation_func)
     msg = f"{transformation_func} is deprecated"
     with tm.assert_produces_warning(warn, match=msg):
         result = gb.transform(transformation_func, *args)
-    if dropna and transformation_func == "fillna":
-        # GH#46369 - result name is the group; remove this block when fixed.
-        tm.assert_equal(result, expected, check_names=False)
-        # This should be None
-        assert result.name == 1.0
-    else:
-        tm.assert_equal(result, expected)
+
+    tm.assert_equal(result, expected)