Does the same apply when using MySQL through ssh using show databases; ?
If it does, it would seem to indicate a problem with MySQL's permissions and not specificaly phpMyAdmin.
If that's the case, login to phpmyadmin as root or da_admin, and make sure that each user only has privileges over his own databases.
I am not aware of anything in phpmyadmin that could cause this, but if the above is not true, and it is only a problem with phpMyAdmin, you might try reinstalling it being sure to use the configuration script DirectAdmin provides.