When historians’ subject is Byzantine history and not Roman history any more?
Does it start with Constantine I and the transition of capital to New Rome aka Constantinople?
With Theodosius and the split to East Roman Empire and West Roman Empire?
With Heraclius who lost Balkans, Syria and Egypt and remained with the Greeks only?
You're not going to get a firm answer on when it 'officially' starts, because it's really a matter of preference. /u/tiako had a post here about some of the boundaries you can make: https://www.reddit.com/r/AskHistorians/comments/14oins/at_what_point_did_the_eastern_roman_empire_become/c7f2ago/
Given that the population of the Roman Empire/Byzantine Empire considered themselves Roman, and there's no firm date you can say it has a gap/end - the distinction, for us, mostly comes from a useful distinction - to distinguish between the medieval state (Byzantium) and its earlier forms (late imperial era, principate, etc)