The $bb->name setting in config.php is the name for the whole site and the name you see in Admin > Content > Forum is the name of the categories or sub-forums (however you want to think about it – see the bottom of http://bbPress.org/forums/ for “Installation”, “Troubleshooting”, “Themes”, etc – that is what you’re changing in Admin > Content > Forums). Changing it there does indeed change the display (look at the bottom of the front page to see the name you are changing in the admin panel: it’s under “Forums”). If it’s not working like that in your installation, there’s another problem I’m not familiar with.
Anyway, being able to change the site name in the admin panel might be a good suggestion. You can make feature requests at http://trac.bbpress.org .
If you deleted the WordPress database and your your bbPress installation was in the same database, then your bbPress installation is gone. You might restore from backup, but other than that you need to reinstall fresh.