I've talked about this issue before, but essentially, in my view, it comes down to whether you think it's useful to have a distinct term to describe a different phase of the same empire. Because, inevitably, there were huge differences between say, the empire of 1000 and the empire of Constantine, let alone that of Augustus. It is hard to pinpoint a specific turning-point, and I actually think that it's impossible to reach a consensus on this, but it is a useful way to distinguish between different stages of the history of the empire nonetheless.

It's also important to point out that in addition to historians using 'Byzantine empire' in their work, the term 'later Roman empire' is often applied to the empire in late antiquity as well, so if we are to shake up the system, we have to reconfigure scholarship across many fields - it would be a bit annoying to extend the 'late' Roman empire from the fourth century all the way to the fifteenth century to say the least. It's the same with AD/BC and CE/BCE, ideally we would have a dating system that would not favour one religious belief over others, but it's simply not realistic to change it and all sensible historians nowadays are very capable of not letting the fact that they are using 'AD' to affect their work on other religions/regions. Byzantium is the same, everyone who works on the field knows that it is only a word meant to denote the last thousand years or so of the Roman empire, a word used without any prejudice or bias, so do we really need a different word if this is the case?