Fix blueprint renaming

This ensures that if a blueprint is renamed at the time of
registration that name is used when constructing endpoints, as
expected.

src/flask/blueprints.py

@@ -67,6 +67,7 @@ def __init__(
         #: blueprint.
         self.url_prefix = url_prefix
 
+        self.name = self.options.get("name", blueprint.name)
         self.name_prefix = self.options.get("name_prefix", "")
 
         #: A dictionary with URL defaults that is added to each and every
@@ -96,9 +97,10 @@ def add_url_rule(
         defaults = self.url_defaults
         if "defaults" in options:
             defaults = dict(defaults, **options.pop("defaults"))
+
         self.app.add_url_rule(
             rule,
-            f"{self.name_prefix}.{self.blueprint.name}.{endpoint}".lstrip("."),
+            f"{self.name_prefix}.{self.name}.{endpoint}".lstrip("."),
             view_func,
             defaults=defaults,
             **options,

tests/test_blueprints.py

@@ -889,3 +889,25 @@ def test_self_registration(app, client) -> None:
     bp = flask.Blueprint("bp", __name__)
     with pytest.raises(ValueError):
         bp.register_blueprint(bp)
+
+
+def test_blueprint_renaming(app, client) -> None:
+    bp = flask.Blueprint("bp", __name__)
+    bp2 = flask.Blueprint("bp2", __name__)
+
+    @bp.get("/")
+    def index():
+        return flask.request.endpoint
+
+    @bp2.get("/")
+    def index2():
+        return flask.request.endpoint
+
+    bp.register_blueprint(bp2, url_prefix="/a", name="sub")
+    app.register_blueprint(bp, url_prefix="/a")
+    app.register_blueprint(bp, url_prefix="/b", name="alt")
+
+    assert client.get("/a/").data == b"bp.index"
+    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"