diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index bce6a735b7b07..fdc7a5b796685 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -323,6 +323,7 @@ Reshaping
 - Bug in :meth:`DataFrame.pivot_table` with ``aggfunc='count'`` or ``aggfunc='sum'`` returning ``NaN`` for missing categories when pivoted on a ``Categorical``. Now returning ``0`` (:issue:`31422`)
 - Bug in :func:`union_indexes` where input index names are not preserved in some cases. Affects :func:`concat` and :class:`DataFrame` constructor (:issue:`13475`)
 - Bug in func :meth:`crosstab` when using multiple columns with ``margins=True`` and ``normalize=True`` (:issue:`35144`)
+- Bug in :meth:`DataFrame.agg` with ``func={'name':<FUNC>}`` incorrectly raising ``TypeError`` when ``DataFrame.columns==['Name']`` (:issue:`36212`)
 -
 
 Sparse
diff --git a/pandas/core/base.py b/pandas/core/base.py
index 1926803d8f04b..7bcce695d999e 100644
--- a/pandas/core/base.py
+++ b/pandas/core/base.py
@@ -470,9 +470,12 @@ def is_any_frame() -> bool:
             try:
                 result = DataFrame(result)
             except ValueError:
-
                 # we have a dict of scalars
-                result = Series(result, name=getattr(self, "name", None))
+
+                # GH 36212 use name only if self is a series
+                name = self.name if (self.ndim == 1) else None
+
+                result = Series(result, name=name)
 
             return result, True
         elif is_list_like(arg):
diff --git a/pandas/tests/frame/apply/test_frame_apply.py b/pandas/tests/frame/apply/test_frame_apply.py
index 1662f9e2fff56..f75d7c13665f9 100644
--- a/pandas/tests/frame/apply/test_frame_apply.py
+++ b/pandas/tests/frame/apply/test_frame_apply.py
@@ -1147,6 +1147,21 @@ def test_demo(self):
         )
         tm.assert_frame_equal(result.reindex_like(expected), expected)
 
+    def test_agg_with_name_as_column_name(self):
+        # GH 36212 - Column name is "name"
+        data = {"name": ["foo", "bar"]}
+        df = pd.DataFrame(data)
+
+        # result's name should be None
+        result = df.agg({"name": "count"})
+        expected = pd.Series({"name": 2})
+        tm.assert_series_equal(result, expected)
+
+        # Check if name is still preserved when aggregating series instead
+        result = df["name"].agg({"name": "count"})
+        expected = pd.Series({"name": 2}, name="name")
+        tm.assert_series_equal(result, expected)
+
     def test_agg_multiple_mixed_no_warning(self):
         # GH 20909
         mdf = pd.DataFrame(