I tried to implement feature requested here: https://sourceforge.net/tracker/?func=detail&aid=3141575&group_id=23067&atid=377411
With this patch phpMyAdmin is showing list of last 10 used databases for logged user on main page.
Feature can be turned on and off by $cfg['Servers'][$i]['dbhistory'] = 'pma_db_history'; in config.inc.php.
User has to create the needed table with the script/create_tables.sql.
User has to create a pma user and give access to this table.
Alternatively you can pull phpmyadmin with this patch from branch "db" I made:
This is my firs finished patch here so any opinion is appreciated.