1. Create a newly named database
2. Dump & import
3. Drop the old database

The most important step: To get going with this, first create a full backup of your MySQL database to make sure you don't loose any data!

#Create a newly named database

This step involves creating the database you want to rename the old database to:

CREATE DATABASE `NEW_DATABASE_NAME`;

#Dump & import

Dump and import the old database into your new database:

mysqldump -u USERNAME -p OLD_DATABASE_NAME | mysql -u USERNAME -p NEW_DATABASE_NAME

#Drop the old database

If your really sure, you can (with the backup on hand) remove the old database safely:

DROP DATABASE `OLD_DATABASE_NAME`