How to rename a database?

sp_renamedb is the stored proc that can be used. The problem you might encountered is the exclusive lock might not be assigned properly. The best practice is to set the db to single user mode before changing its name and back to multi-user mode afterwards.

ALTER DATABASE old_db_name
SET SINGLE_USER WITH ROLLBACK IMMEDIATE
GO
SP_RENAMEDB old_db_name, new_db_name
Go
ALTER DATABASE new_db_name
SET MULTI_USER
GO