The Roman Senate continued to sit throughout the period of the Fall of Rome, so we might well refer to this as the Fall of the Western Roman Empire and the return of the Etruscan Roman Kingdom (with a probable German as King over Italy and FYR).
The Eastern Roman Empire didn't fall. Beginning in 535, though, everybody had some serious problems with a total economic collapse North of the Mediterranean, and some serious population drops in a variety of places.
You can argue there was still an Eastern Roman Empire. You can point out that a part of France (The Domain of Soissons) remained Roman for another decade. You can note that Eastern Romans actually managed to recapture Rome in 540.
But, really, in 476 it was over.