phpmyadmin don't see new created databases

If you Still don't see it, Try to logout from cpanel and then log in again to cPanel or PHPMyAdmin. It worked for me.

You need to give your user access to that database, log into phpMyAdmin as the mysql administrator, go to the database in question and click on "permissions", then proceed to add your desired users to the database. Alternatively you can use the mysql client and issue the commands as SQL such as:

GRANT ALL ON db1.* TO 'finn'@'localhost';