The name of the MYSQL database has a prefix which is the cpanel username and is followed by _ and then the actual database name. So if you need to change the whole database name you have to rename the cpanel username which is not recommended and the database name.
Inorder for a change the username, you have to modify the account by changing the username you want by logging into whm with user root.This means you have to edit web files,MYSQL data bases of the account.That is why it is recommended not to change the username but you can change the database name by creating a new database and import old database into it.