You have to use database.sql file and import it using database management tool provided by your hosting company, which, most likely, is phpMyAdmin. That action replaces "install database" button in setup utility, but you still have to let RadioDJ know your connection settings.
You can use any database name, as long as you use the same name in database setup utility, which updates settings_database.xml file in main RadioDJ directory. In fact, you can edit the xml file and fill in your connection settings there. That should be done while RadioDJ is not running, of course.
I suggest to create a separate database for RadioDJ instead of using existing one with other data already in it. It would make maintenance task easier.