We have a bare bones "app" on Facebook, mostly so we can allow users to login to our site with FB. We also include a Like button on our site; right now the Like button points to our app profile page, where we occasionally post updates for our users.
Our app profile page has a couple dozen Likes now, so we were hoping to be able to give the page a short user name like http://www.facebook.com/blahblah.
Is there a way to get a user name for our app? (I know it's possible to claim an URL on apps.facebook.com if we implement a Canvas page, but we don't have a Canvas app and don't see why we would.)