The best and safe way to rename MySQL database is presented as follows.
You can create a new database exactly as the previous database existed and then drop the old database when you're done.
Use the mysqldump tool to create a .sql backup of the database via mysqldump orig_db > orig_db.sql
or if you need to use a username and password then run mysqldump -u root -p orig_db > orig_db.sql.
orig_db is the name of the database you want to "rename", root would be the user you're logging in as and orig_db.sql would be the file created containing the backup. Now create a new, empty database with the name you want for the database.
For example, mysql -u root -p -e "create database new_db". Once that's done, then runmysql -u root -p new_db < orig_db.sql. new_db now exists as a perfect copy of orig_db.
You can then drop the original database as you now have it existing in the new database with the database name you wanted.
The short, quick steps without all the above explanation are: