/config/blesta-new.php is used for new installs and upgrades in order to write /config/blesta.php. If uploading an upgrade, it will be overwritten. However, /config/blesta.php should NEVER be overwritten or renamed manually. It contains very important information, including a system key that is CRITICAL it remain unchanged.
It's perfectly fine to have a /config/blesta.php and /config/blesta-new.php on your server. There are no blesta.ini files though.