diff --git a/pandas/core/groupby/ops.py b/pandas/core/groupby/ops.py
index e438db6c620ec..b59c7b4cb1cea 100644
--- a/pandas/core/groupby/ops.py
+++ b/pandas/core/groupby/ops.py
@@ -343,7 +343,7 @@ def get_group_levels(self):
 
     _cython_arity = {"ohlc": 4}  # OHLC
 
-    _name_functions = {"ohlc": lambda *args: ["open", "high", "low", "close"]}
+    _name_functions = {"ohlc": ["open", "high", "low", "close"]}
 
     def _is_builtin_func(self, arg):
         """
@@ -399,6 +399,13 @@ def _cython_operation(
         assert kind in ["transform", "aggregate"]
         orig_values = values
 
+        if values.ndim > 2:
+            raise NotImplementedError("number of dimensions is currently limited to 2")
+        elif values.ndim == 2:
+            # Note: it is *not* the case that axis is always 0 for 1-dim values,
+            #  as we can have 1D ExtensionArrays that we need to treat as 2D
+            assert axis == 1, axis
+
         # can we do this operation with our cython functions
         # if not raise NotImplementedError
 
@@ -524,10 +531,7 @@ def _cython_operation(
         if vdim == 1 and arity == 1:
             result = result[:, 0]
 
-        if how in self._name_functions:
-            names = self._name_functions[how]()  # type: Optional[List[str]]
-        else:
-            names = None
+        names = self._name_functions.get(how, None)  # type: Optional[List[str]]
 
         if swapped:
             result = result.swapaxes(0, axis)
@@ -557,10 +561,7 @@ def _aggregate(
         is_datetimelike: bool,
         min_count: int = -1,
     ):
-        if values.ndim > 2:
-            # punting for now
-            raise NotImplementedError("number of dimensions is currently limited to 2")
-        elif agg_func is libgroupby.group_nth:
+        if agg_func is libgroupby.group_nth:
             # different signature from the others
             # TODO: should we be using min_count instead of hard-coding it?
             agg_func(result, counts, values, comp_ids, rank=1, min_count=-1)
@@ -574,11 +575,7 @@ def _transform(
     ):
 
         comp_ids, _, ngroups = self.group_info
-        if values.ndim > 2:
-            # punting for now
-            raise NotImplementedError("number of dimensions is currently limited to 2")
-        else:
-            transform_func(result, values, comp_ids, ngroups, is_datetimelike, **kwargs)
+        transform_func(result, values, comp_ids, ngroups, is_datetimelike, **kwargs)
 
         return result