Should the Byzantium empire be renamed as it makes little historical sense referring to them thus?

There could be many reasons why it was called The Byzantine Empire. Maybe it came into use by historians, so that the period of the single 'Roman Empire', up until 475 a.d., and the era of the 'Eastern Roman Empire' were not to be confused. The Ottoman Sultans called themselves Roman Emperor so more than anything the term probably derived to give distinction to the Dynasty rather than the Empire. They themselves called it the 'Eastern Roman Empire', but of course Byzantium was the Greek name for the ancient city of Constantinople, and that is where the name originated so in some ways it does make sense. Most importantly though their were the Holy Roman Emperors, I have a theory that they were referred to as the byzantines to prevent confusion between the 'Holy Romans' and the 'Eastern Romans', and perhaps also to avoid a clash in titles, 'Byzantine Emperor' vs 'Holy Roman Emperor' of course.