This seems to be a common problem with cPanel. The passwords for cPanel and MySQL get out of sync. Hopefull the solutions here will work for you.
I need to write an article about this and do the following:
forums.cpanel.net/threads/acces-phpmyadmin-asking-username-a...
usually if i acces phpmyadmin from cpanel, it always directly to phpmyadmin page, but suddenly if i acces phpmyadmin it asking username and password .....
wiki.knownhost.com/control-panels/cpanel-whm/i-am-unable-to-...
phpMyAdmin is asking for a password to login. To fix this problem, you need to reset the cPanel password as follows:
kb.canvashost.com/?ht_kb=why-does-the-phpmyadmin-link-in-cpa...
When logged into cPanel, most users can simply click on the PHPMyAdmin icon to directly access their MySQL databases. Sometimes, however, the user is taken to the PHPMyAdmin login screen again, where they are prompted to enter a username and password.< ...