You won't need to reregister the car, if it was a lease yes because the lease holder owns it, if its a finance you "own" the car so the registration is to you. All they would do is VW credit would send a letter saying it was paid off and the new bank would send a letter saying they now have the lien. If your registration card says anything about the lien they would just send you a new card shouldn't be anything you have to do. You are the "owner" and that doesn't change.