diff --git a/rdflib/graph.py b/rdflib/graph.py
index 80ccc3fa8..b2b9d410c 100644
--- a/rdflib/graph.py
+++ b/rdflib/graph.py
@@ -472,6 +472,14 @@ def store(self) -> Store:
     def identifier(self) -> _ContextIdentifierType:
         return self.__identifier
 
+    @identifier.setter
+    def identifier(self, identifier: IdentifiedNode):
+        if not isinstance(identifier, IdentifiedNode):
+            raise TypeError(
+                "The identifier for a Graph must be an IdentifiedNode"
+            )
+        self.__identifier = identifier
+
     @property
     def namespace_manager(self) -> NamespaceManager:
         """
@@ -2535,6 +2543,13 @@ def add_graph(
         """alias of graph for consistency"""
         return self.graph(g)
 
+    def add_named_graph(
+            self, named_graph_identifier: IdentifiedNode, g: Optional[Union[_ContextIdentifierType, _ContextType, str]]
+    ) -> Graph:
+        new_g = self.graph(g)
+        new_g.identifier = named_graph_identifier
+        return new_g
+
     def remove_graph(
         self: _DatasetT, g: Optional[Union[_ContextIdentifierType, _ContextType, str]]
     ) -> _DatasetT:
diff --git a/test/test_graph/test_graph.py b/test/test_graph/test_graph.py
index 639aa710c..ebaa1d759 100644
--- a/test/test_graph/test_graph.py
+++ b/test/test_graph/test_graph.py
@@ -45,6 +45,17 @@ def test_property_identifier() -> None:
     assert id == graph.identifier
 
 
+def test_property_setter_identifier() -> None:
+    """
+    The ``identifier`` property setter works correctly.
+    """
+    id = URIRef("example:a")
+    new_id = URIRef("example:b")
+    graph = Graph(identifier=id)
+    assert id == graph.identifier
+    graph.identifier = new_id
+    assert new_id == graph.identifier
+
 def test_property_namespace_manager() -> None:
     """
     The ``namespace_manager`` property works correctly.