Changing what exists.
RENAMING
cPanel offers a rename function under MySQL Databases.
It works, and the application will stop until you update its configuration to the new name.
Update the configuration in the same session, or you will forget why the site broke.
For anything important, take a backup first. Renaming involves copying data.
REMOVING
Only when you are certain nothing uses it.
- Back it up first and download the dump. This is not optional; deletion is permanent.
- cPanel > MySQL Databases, find it, and delete.
- Delete its user as well, if nothing else uses that user.
CHECKING NOTHING USES IT
Search your applications' configuration files for the database name.
With several sites on one account, deleting the wrong database is a real risk.
AFTER REMOVING AN APPLICATION
Remove the database and the user along with the files. Leaving them consumes your database allowance and your disk.
Accounts commonly hold databases for applications removed years ago.