I think the term Byzantium is wrong

I’ve always loved the eastern Roman Empire’s history. It’s always been an under appreciated facet of European and indeed Middle Eastern history and could even be said its death was the end of an epoch. But I’ve never agreed with the term Byzantium for the Eastern Romans and how Edward Gibbon coined it as such.

They were the successors of the institutions of the Roman Empire and called themselves romans. They were comprised of many groups thought it’s history but spoke Greek. The city of Constantinople which was the key asset of the empire has not been called Byzantium in eons either.

I always thought ERE (Eastern Romans Empire), or the empire of Constantinople would make more sense because one referred to its legal legacy and what’s its inhabitants and neighbours called it and the the latter because the city was key to its identity and survival.

What do you all think?