The database created in CPanel does not show in phpMyAdmin?
Once you created your database just logout from your Cpanel. Then you can again login on Cpanel and go to phpmyadmin. Your newly created database would be there.
Solved! For the people who may see the same issue here how it was resolved:
1 - Create a new database by completing the CPanel`s wizard->check phpmyadmin, if it does not show up continue with step 2,
2 - Close phpmyadmin,
3 - Logout CPanel,
4 - Login to CPanel again
5 - Open phpmyadmin->the new database is there!