I realize the obvious answers to this are that they did not hold the city of Rome for most of that era and that their capital during that era was the city formerly known as Byzantium. However, they always referred to themselves as the Roman Empire (Empire of Romans if you want to literally translate), while outsiders tended to as well with the exception of some nations in the West as far as I know.
So building on my question, how is it that "Byzantine Empire" came to be the dominant term? Is this common across most languages, or is it something particular to English? Finally, will this ever change? I have noticed a few historians starting to refer to it as the Roman Empire instead.
In English history (based on a Western European concept), the "Roman Empire" fell when Rome fell. In 476 AD, to be exact, when the last Roman "emperor" of Romulus Augustulus steps down and the naming of Odoacer as "king", thus ending the western Roman "Empire." The subsequent history of western Europe embarks on the Age of Faith, and the rise of the Holy Roman Empire, the consolidation of Gaul under the Franks, the battles for Italy, Sicily and Iberia. All the while the Eastern Roman empire continues on.
It is simply a way to distinguish the Roman Empire of Caesar, Augustus, Claudius, Marcus Aurelius, etc. with an Emperor based in Rome with the subsequent formation of an Empire with the Emperor only in Constantinople/Byzantium.
So, instead of saying the "Roman Empire with the Emperor in Rome" or the "Roman Empire with the Emperor in Constantinople", you can just easily say "the Roman Empire" or the "Byzantium Empire" and save syllables.
I remember having a discussion regarding religion, and he stated Christianity is the death of Empires, as it took less than 70 years to collapse the Roman Empire. To which I replied, "70 plus another 1100 years when the Turks finally took Constantinople." Which he had no idea that the "Byzantium Empire" was simply the Roman Empire (same laws, etc.) moved to a new capitol.
I think that the distinguishing of the two names, while convenient, ignore the true effect of the Roman Empire, and create unintended ignorance in the western European (and by extension - North American) world. It merely reflects the western European bias of judging history that occurred to their lands and people as more important than history to others. This is quite common and ordinary to have self-centered historical bias.
hi! you may be interested in these earlier posts. Hopefully someone can address your question about trends in current historiography.