Can I use PHPMyAdmin to create, alter, and change databases and their permissions via PHPMyAdmin?
Unfortunately, this is not the intended functionality of cPanel and the preconfigured settings for PHPMyAdmin. You would need to install your version of PHPMyAdmin to perform those changes manually.
cPanel would not support this, and you would need to contact your system administrator for more direct assistance performing this task.
You will be able to review the following forum post where this is discussed.
Additionally, you can request this functionality be added via the following feature request.
You would be able to create a database via the WHM API calls via command-line. This is one of the approved ways to create a database for a user. The following excerpt shows how to create a database. You would substitute in your information for the user and name entries.
-bash-4.2# uapi --user=cptest Mysql create_database name=cptest_testdb