Amazon: How to change database name in Amazon RDS MySQL?
you can rename the database using the following command but make sure to take backup first

CREATE database new_db_name;
RENAME TABLE db_name.table1 TO new_db_name, db_name.table2 TO new_db_name;
DROP database db_name;


references:
http://www.rndblog.com/how-to-rename-a-database-in-mysql/
https://stackoverflow.com/questions/12190000/rename-mysql-database