diff --git a/graphene/types/schema.py b/graphene/types/schema.py
index c1c8e825..be40bd6a 100644
--- a/graphene/types/schema.py
+++ b/graphene/types/schema.py
@@ -296,8 +296,7 @@ class GrapheneGraphQLSchema(GraphQLSchema):
             graphene_type=type_,
             name=type_._meta.name,
             description=type_._meta.description,
-            # TODO: container_type not supported by core-next (is this needed?)
-            # container_type=type_._meta.container,
+            out_type=type_._meta.container,
             fields=partial(
                 self.construct_fields_for_type, map_, type_, is_input_type=True
             ),
@@ -345,8 +344,7 @@ class GrapheneGraphQLSchema(GraphQLSchema):
                 _field = GraphQLInputField(
                     field_type,
                     default_value=field.default_value,
-                    # TODO: out_name not (yet) supported by core-next
-                    # out_name=name,
+                    out_name=name,
                     description=field.description,
                 )
             else:
@@ -357,8 +355,7 @@ class GrapheneGraphQLSchema(GraphQLSchema):
                     processed_arg_name = arg.name or self.get_name(arg_name)
                     args[processed_arg_name] = GraphQLArgument(
                         arg_type,
-                        # TODO: out_name not (yet) supported by core-next
-                        # out_name=arg_name,
+                        out_name=arg_name,
                         description=arg.description,
                         default_value=INVALID
                         if isinstance(arg.type, NonNull)
diff --git a/graphene/types/tests/test_inputobjecttype.py b/graphene/types/tests/test_inputobjecttype.py
index a88953bf..de42b66e 100644
--- a/graphene/types/tests/test_inputobjecttype.py
+++ b/graphene/types/tests/test_inputobjecttype.py
@@ -105,7 +105,6 @@ def test_generate_inputobjecttype_inherit_abstracttype_reversed():
     ]
 
 
-# TOOD: I think this fails because container_type is not supported in core-next
 def test_inputobjecttype_of_input():
     class Child(InputObjectType):
         first_name = String()
@@ -134,5 +133,6 @@ def test_inputobjecttype_of_input():
     }
     """
     )
+
     assert not result.errors
     assert result.data == {"isChild": True}
diff --git a/graphene/types/tests/test_type_map.py b/graphene/types/tests/test_type_map.py
index b4d7d6ad..9c4d95fb 100644
--- a/graphene/types/tests/test_type_map.py
+++ b/graphene/types/tests/test_type_map.py
@@ -90,8 +90,7 @@ def test_objecttype():
             GraphQLString,
             description="Argument description",
             default_value="x",
-            # TODO: out_name not (yet) supported by core-next
-            # out_name="bar",
+            out_name="bar",
         )
     }
 
@@ -148,8 +147,7 @@ def test_interface():
             GraphQLString,
             description="Argument description",
             default_value="x",
-            # TODO: out_name not (yet) supported by core-next
-            # out_name="bar",
+            out_name="bar",
         )
     }
 
@@ -182,15 +180,14 @@ def test_inputobject():
 
     other_graphql_type = type_map["OtherObjectType"]
     inner_graphql_type = type_map["MyInnerObjectType"]
-    # TODO: create_container not supported by core-next
-    container = graphql_type.create_container(
+    container = graphql_type.out_type(
         {
             "bar": "oh!",
-            "baz": inner_graphql_type.create_container(
+            "baz": inner_graphql_type.out_type(
                 {
                     "some_other_field": [
-                        other_graphql_type.create_container({"thingy": 1}),
-                        other_graphql_type.create_container({"thingy": 2}),
+                        other_graphql_type.out_type({"thingy": 1}),
+                        other_graphql_type.out_type({"thingy": 2}),
                     ]
                 }
             ),
@@ -235,8 +232,7 @@ def test_objecttype_camelcase():
         "barFoo": GraphQLArgument(
             GraphQLString,
             default_value=None,
-            # TODO: out_name not (yet) supported by core-next
-            # out_name="bar_foo"
+            out_name="bar_foo"
         )
     }
 
@@ -262,8 +258,7 @@ def test_objecttype_camelcase_disabled():
         "bar_foo": GraphQLArgument(
             GraphQLString,
             default_value=None,
-            # TODO: out_name not (yet) supported by core-next
-            # out_name="bar_foo"
+            out_name="bar_foo"
         )
     }