I tried using the rename database command, but it fails with the following error. I don’t see an option to stop the RDS instance via the Amazon RDS console either.
mysql> rename database foo to foo_orig;
ERROR 1064 (42000): You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'database foo to foo_orig' at line 1
From http://dev.mysql.com/doc/refman/5.1/en/rename-database.html
Is too little chance Amazon RDS using version less than 5.2.
If you have the access to mysql server, you can try :-