diff --git a/CHANGES.rst b/CHANGES.rst
index c27b623f..bdfa9f01 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -12,6 +12,7 @@ Unreleased
     decorators to accept functions with no arguments. :issue:`4098`
 -   Support View and MethodView instances with async handlers. :issue:`4112`
 -   Enhance typing of ``app.errorhandler`` decorator. :issue:`4095`
+-   Fix registering a blueprint twice with differing names. :issue:`4124`
 
 
 Version 2.0.1
diff --git a/src/flask/blueprints.py b/src/flask/blueprints.py
index 8241420b..c8ce67a4 100644
--- a/src/flask/blueprints.py
+++ b/src/flask/blueprints.py
@@ -293,7 +293,6 @@ class Blueprint(Scaffold):
             Registering the same blueprint with the same name multiple
             times is deprecated and will become an error in Flask 2.1.
         """
-        first_registration = not any(bp is self for bp in app.blueprints.values())
         name_prefix = options.get("name_prefix", "")
         self_name = options.get("name", self.name)
         name = f"{name_prefix}.{self_name}".lstrip(".")
@@ -318,9 +317,12 @@ class Blueprint(Scaffold):
                     stacklevel=4,
                 )
 
+        first_bp_registration = not any(bp is self for bp in app.blueprints.values())
+        first_name_registration = name not in app.blueprints
+
         app.blueprints[name] = self
         self._got_registered_once = True
-        state = self.make_setup_state(app, options, first_registration)
+        state = self.make_setup_state(app, options, first_bp_registration)
 
         if self.has_static_folder:
             state.add_url_rule(
@@ -330,7 +332,7 @@ class Blueprint(Scaffold):
             )
 
         # Merge blueprint data into parent.
-        if first_registration:
+        if first_bp_registration or first_name_registration:
 
             def extend(bp_dict, parent_dict):
                 for key, values in bp_dict.items():
diff --git a/tests/test_blueprints.py b/tests/test_blueprints.py
index 088ad779..a124c612 100644
--- a/tests/test_blueprints.py
+++ b/tests/test_blueprints.py
@@ -899,6 +899,14 @@ def test_blueprint_renaming(app, client) -> None:
     def index():
         return flask.request.endpoint
 
+    @bp.get("/error")
+    def error():
+        flask.abort(403)
+
+    @bp.errorhandler(403)
+    def forbidden(_: Exception):
+        return "Error", 403
+
     @bp2.get("/")
     def index2():
         return flask.request.endpoint
@@ -911,3 +919,5 @@ def test_blueprint_renaming(app, client) -> None:
     assert client.get("/b/").data == b"alt.index"
     assert client.get("/a/a/").data == b"bp.sub.index2"
     assert client.get("/b/a/").data == b"alt.sub.index2"
+    assert client.get("/a/error").data == b"Error"
+    assert client.get("/b/error").data == b"Error"