diff --git a/mypy/plugin.py b/mypy/plugin.py
index 4cd769427ce19..6f6d4a8df5b98 100644
--- a/mypy/plugin.py
+++ b/mypy/plugin.py
@@ -250,13 +250,13 @@ class SemanticAnalyzerPluginInterface:
     msg: MessageBuilder
 
     @abstractmethod
-    def named_type(self, qualified_name: str, args: Optional[List[Type]] = None) -> Instance:
+    def named_type(self, fullname: str,
+                   args: Optional[List[Type]] = None) -> Instance:
         """Construct an instance of a builtin type with given type arguments."""
         raise NotImplementedError
 
     @abstractmethod
-    def named_type_or_none(self,
-                           qualified_name: str,
+    def named_type_or_none(self, fullname: str,
                            args: Optional[List[Type]] = None) -> Optional[Instance]:
         """Construct an instance of a type with given type arguments.
 
diff --git a/mypy/plugins/attrs.py b/mypy/plugins/attrs.py
index 2dd3403186da6..f6de73f14f982 100644
--- a/mypy/plugins/attrs.py
+++ b/mypy/plugins/attrs.py
@@ -640,8 +640,8 @@ def _parse_assignments(
 
 def _add_order(ctx: 'mypy.plugin.ClassDefContext', adder: 'MethodAdder') -> None:
     """Generate all the ordering methods for this class."""
-    bool_type = ctx.api.named_type('__builtins__.bool')
-    object_type = ctx.api.named_type('__builtins__.object')
+    bool_type = ctx.api.named_type('builtins.bool')
+    object_type = ctx.api.named_type('builtins.object')
     # Make the types be:
     #    AT = TypeVar('AT')
     #    def __lt__(self: AT, other: AT) -> bool
@@ -714,7 +714,7 @@ def _add_attrs_magic_attribute(ctx: 'mypy.plugin.ClassDefContext',
         ctx.api.named_type_or_none('attr.Attribute', [attr_type or any_type]) or any_type
         for attr_type in raw_attr_types
     ]
-    fallback_type = ctx.api.named_type('__builtins__.tuple', [
+    fallback_type = ctx.api.named_type('builtins.tuple', [
         ctx.api.named_type_or_none('attr.Attribute', [any_type]) or any_type,
     ])
     var = Var(name=attr_name, type=TupleType(attributes_types, fallback=fallback_type))
diff --git a/mypy/plugins/common.py b/mypy/plugins/common.py
index df21718d99496..1beb538493272 100644
--- a/mypy/plugins/common.py
+++ b/mypy/plugins/common.py
@@ -122,13 +122,8 @@ def add_method_to_class(
             cls.defs.body.remove(sym.node)
 
     self_type = self_type or fill_typevars(info)
-    # TODO: semanal.py and checker.py seem to have subtly different implementations of
-    # named_type/named_generic_type (starting with the fact that we have to use different names
-    # for builtins), so it's easier to just check which one we're dealing with here and pick the
-    # correct function to use than to try to add a named_type method that behaves the same for
-    # both. We should probably combine those implementations at some point.
     if isinstance(api, SemanticAnalyzerPluginInterface):
-        function_type = api.named_type('__builtins__.function')
+        function_type = api.named_type('builtins.function')
     else:
         function_type = api.named_generic_type('builtins.function', [])
 
diff --git a/mypy/plugins/dataclasses.py b/mypy/plugins/dataclasses.py
index 5f149713cd39c..62e3279eac1e2 100644
--- a/mypy/plugins/dataclasses.py
+++ b/mypy/plugins/dataclasses.py
@@ -145,7 +145,7 @@ def transform(self) -> None:
         if (decorator_arguments['eq'] and info.get('__eq__') is None or
                 decorator_arguments['order']):
             # Type variable for self types in generated methods.
-            obj_type = ctx.api.named_type('__builtins__.object')
+            obj_type = ctx.api.named_type('builtins.object')
             self_tvar_expr = TypeVarExpr(SELF_TVAR_NAME, info.fullname + '.' + SELF_TVAR_NAME,
                                          [], obj_type)
             info.names[SELF_TVAR_NAME] = SymbolTableNode(MDEF, self_tvar_expr)
@@ -158,10 +158,10 @@ def transform(self) -> None:
             for method_name in ['__lt__', '__gt__', '__le__', '__ge__']:
                 # Like for __eq__ and __ne__, we want "other" to match
                 # the self type.
-                obj_type = ctx.api.named_type('__builtins__.object')
+                obj_type = ctx.api.named_type('builtins.object')
                 order_tvar_def = TypeVarType(SELF_TVAR_NAME, info.fullname + '.' + SELF_TVAR_NAME,
                                             -1, [], obj_type)
-                order_return_type = ctx.api.named_type('__builtins__.bool')
+                order_return_type = ctx.api.named_type('builtins.bool')
                 order_args = [
                     Argument(Var('other', order_tvar_def), order_tvar_def, None, ARG_POS)
                 ]
@@ -426,8 +426,8 @@ def _add_dataclass_fields_magic_attribute(self) -> None:
         attr_name = '__dataclass_fields__'
         any_type = AnyType(TypeOfAny.explicit)
         field_type = self._ctx.api.named_type_or_none('dataclasses.Field', [any_type]) or any_type
-        attr_type = self._ctx.api.named_type('__builtins__.dict', [
-            self._ctx.api.named_type('__builtins__.str'),
+        attr_type = self._ctx.api.named_type('builtins.dict', [
+            self._ctx.api.named_type('builtins.str'),
             field_type,
         ])
         var = Var(name=attr_name, type=attr_type)
diff --git a/mypy/plugins/functools.py b/mypy/plugins/functools.py
index e7f90acc99fe7..e52d478927e8c 100644
--- a/mypy/plugins/functools.py
+++ b/mypy/plugins/functools.py
@@ -45,9 +45,9 @@ def functools_total_ordering_maker_callback(ctx: mypy.plugin.ClassDefContext,
         return
 
     other_type = _find_other_type(root_method)
-    bool_type = ctx.api.named_type('__builtins__.bool')
+    bool_type = ctx.api.named_type('builtins.bool')
     ret_type: Type = bool_type
-    if root_method.type.ret_type != ctx.api.named_type('__builtins__.bool'):
+    if root_method.type.ret_type != ctx.api.named_type('builtins.bool'):
         proper_ret_type = get_proper_type(root_method.type.ret_type)
         if not (isinstance(proper_ret_type, UnboundType)
                 and proper_ret_type.name.split('.')[-1] == 'bool'):
diff --git a/mypy/semanal.py b/mypy/semanal.py
index e710c5946386e..555f04a69a62c 100644
--- a/mypy/semanal.py
+++ b/mypy/semanal.py
@@ -4411,13 +4411,13 @@ def builtin_type(self, fully_qualified_name: str) -> Instance:
         return Instance(node, [AnyType(TypeOfAny.special_form)] * len(node.defn.type_vars))
 
     def object_type(self) -> Instance:
-        return self.named_type('__builtins__.object')
+        return self.named_type('builtins.object')
 
     def str_type(self) -> Instance:
-        return self.named_type('__builtins__.str')
+        return self.named_type('builtins.str')
 
-    def named_type(self, qualified_name: str, args: Optional[List[Type]] = None) -> Instance:
-        sym = self.lookup_qualified(qualified_name, Context())
+    def named_type(self, fullname: str, args: Optional[List[Type]] = None) -> Instance:
+        sym = self.lookup_fully_qualified(fullname)
         assert sym, "Internal error: attempted to construct unknown type"
         node = sym.node
         assert isinstance(node, TypeInfo)
@@ -4426,9 +4426,9 @@ def named_type(self, qualified_name: str, args: Optional[List[Type]] = None) ->
             return Instance(node, args)
         return Instance(node, [AnyType(TypeOfAny.special_form)] * len(node.defn.type_vars))
 
-    def named_type_or_none(self, qualified_name: str,
+    def named_type_or_none(self, fullname: str,
                            args: Optional[List[Type]] = None) -> Optional[Instance]:
-        sym = self.lookup_fully_qualified_or_none(qualified_name)
+        sym = self.lookup_fully_qualified_or_none(fullname)
         if not sym or isinstance(sym.node, PlaceholderNode):
             return None
         node = sym.node
diff --git a/mypy/semanal_infer.py b/mypy/semanal_infer.py
index 25244169b2c44..73a1077c57886 100644
--- a/mypy/semanal_infer.py
+++ b/mypy/semanal_infer.py
@@ -30,7 +30,7 @@ def infer_decorator_signature_if_simple(dec: Decorator,
                 [ARG_POS],
                 [None],
                 AnyType(TypeOfAny.special_form),
-                analyzer.named_type('__builtins__.function'),
+                analyzer.named_type('builtins.function'),
                 name=dec.var.name)
         elif isinstance(dec.func.type, CallableType):
             dec.var.type = dec.func.type
@@ -47,7 +47,7 @@ def infer_decorator_signature_if_simple(dec: Decorator,
     if decorator_preserves_type:
         # No non-identity decorators left. We can trivially infer the type
         # of the function here.
-        dec.var.type = function_type(dec.func, analyzer.named_type('__builtins__.function'))
+        dec.var.type = function_type(dec.func, analyzer.named_type('builtins.function'))
     if dec.decorators:
         return_type = calculate_return_type(dec.decorators[0])
         if return_type and isinstance(return_type, AnyType):
@@ -58,7 +58,7 @@ def infer_decorator_signature_if_simple(dec: Decorator,
         if sig:
             # The outermost decorator always returns the same kind of function,
             # so we know that this is the type of the decorated function.
-            orig_sig = function_type(dec.func, analyzer.named_type('__builtins__.function'))
+            orig_sig = function_type(dec.func, analyzer.named_type('builtins.function'))
             sig.name = orig_sig.items[0].name
             dec.var.type = sig
 
diff --git a/mypy/semanal_namedtuple.py b/mypy/semanal_namedtuple.py
index b543057104eca..8930c63d2bef6 100644
--- a/mypy/semanal_namedtuple.py
+++ b/mypy/semanal_namedtuple.py
@@ -384,19 +384,19 @@ def build_namedtuple_typeinfo(self,
                                   types: List[Type],
                                   default_items: Mapping[str, Expression],
                                   line: int) -> TypeInfo:
-        strtype = self.api.named_type('__builtins__.str')
+        strtype = self.api.named_type('builtins.str')
         implicit_any = AnyType(TypeOfAny.special_form)
-        basetuple_type = self.api.named_type('__builtins__.tuple', [implicit_any])
+        basetuple_type = self.api.named_type('builtins.tuple', [implicit_any])
         dictype = (self.api.named_type_or_none('builtins.dict', [strtype, implicit_any])
-                   or self.api.named_type('__builtins__.object'))
+                   or self.api.named_type('builtins.object'))
         # Actual signature should return OrderedDict[str, Union[types]]
         ordereddictype = (self.api.named_type_or_none('builtins.dict', [strtype, implicit_any])
-                          or self.api.named_type('__builtins__.object'))
-        fallback = self.api.named_type('__builtins__.tuple', [implicit_any])
+                          or self.api.named_type('builtins.object'))
+        fallback = self.api.named_type('builtins.tuple', [implicit_any])
         # Note: actual signature should accept an invariant version of Iterable[UnionType[types]].
         # but it can't be expressed. 'new' and 'len' should be callable types.
         iterable_type = self.api.named_type_or_none('typing.Iterable', [implicit_any])
-        function_type = self.api.named_type('__builtins__.function')
+        function_type = self.api.named_type('builtins.function')
 
         info = self.api.basic_new_typeinfo(name, fallback, line)
         info.is_named_tuple = True
diff --git a/mypy/semanal_newtype.py b/mypy/semanal_newtype.py
index 4d5077dbfe433..047df3d85b83d 100644
--- a/mypy/semanal_newtype.py
+++ b/mypy/semanal_newtype.py
@@ -84,7 +84,7 @@ def process_newtype_declaration(self, s: AssignmentStmt) -> bool:
                 self.fail(message.format(format_type(old_type)), s, code=codes.VALID_NEWTYPE)
             # Otherwise the error was already reported.
             old_type = AnyType(TypeOfAny.from_error)
-            object_type = self.api.named_type('__builtins__.object')
+            object_type = self.api.named_type('builtins.object')
             newtype_class_info = self.build_newtype_typeinfo(name, old_type, object_type, s.line)
             newtype_class_info.fallback_to_any = True
 
@@ -194,7 +194,7 @@ def build_newtype_typeinfo(self, name: str, old_type: Type, base_type: Instance,
             arg_kinds=[arg.kind for arg in args],
             arg_names=['self', 'item'],
             ret_type=NoneType(),
-            fallback=self.api.named_type('__builtins__.function'),
+            fallback=self.api.named_type('builtins.function'),
             name=name)
         init_func = FuncDef('__init__', args, Block([]), typ=signature)
         init_func.info = info
diff --git a/mypy/semanal_shared.py b/mypy/semanal_shared.py
index 6b0fe12516934..43ce1bb592145 100644
--- a/mypy/semanal_shared.py
+++ b/mypy/semanal_shared.py
@@ -101,11 +101,12 @@ def lookup(self, name: str, ctx: Context,
         raise NotImplementedError
 
     @abstractmethod
-    def named_type(self, qualified_name: str, args: Optional[List[Type]] = None) -> Instance:
+    def named_type(self, fullname: str,
+                   args: Optional[List[Type]] = None) -> Instance:
         raise NotImplementedError
 
     @abstractmethod
-    def named_type_or_none(self, qualified_name: str,
+    def named_type_or_none(self, fullname: str,
                            args: Optional[List[Type]] = None) -> Optional[Instance]:
         raise NotImplementedError