Their normal procedure is to complete the FBI name check before the interview is scheduled, although a small percentage of applicants still get interviewed without the name check being completed.
However, they definitely would not have recommended you for approval if the FBI name check was still pending. So you can be confident that you don't have to worry about the name check at this stage; you just have to wait for them to complete the formalities to schedule you for an oath ceremony and send the oath letter.