First of all, more than one person may use the device (think a family with an iPad) so what your doing is inherently a bad idea.
That said, you can use an in-app purchase to let them buy account access - check with the server first to make sure a desired username is available, then let them use an in-app purchase to buy access, and on your server tie that purchase ID to the user name. Even if they deleted the app and tried to re-purchase (while logged into the same iTunes store account) it would see a purchase had been made and essentially be the same user. It even does kind of work with multiple users as they could switch iTunes accounts (though that is a pain).
I would also suggest trying to tie it to the users iCloud account in some way, which is easier for users to switch between on an device (a family might use one iTunes account but have separate iCloud accounts).
If you don't want to give Apple 30% of the registration fee, your only option is to have users sign up on the web and pay there, then have a login they can use in your app. Then it's a matter of trying to prevent duplicate logins on you server, although as a last point of thought, I can't remember a business that succeeded by refusing people's money.