I don't think Americans would consider that America, and in particular, if the government had changed from the old forms, to a dictatorship, with a different language, and new religion. Plus upholding this new religion as the "law of the land" with even more lurid punishments, such as being strapped under a donkey, after your eyes gouged out. If someone wrote a book a thousand years later, separating, or conflating the two, that is fine in its own way. A lot of history is just invention for propaganda purposes, iirc it's Napoleon that says history is a lie agreed upon. I listened to an interview with a historian as well that said even if institutions bear the same name, really 200 years later they are completely different, and it is people liking to think they are similar, that is more important.
I recently helped a young women with her history work, about the Ukraine in 1945, and she had a translated work by an American, of documents from the main archives in Podolsk. They also had the originals published, and some, due to being hand copied, or whatever, except the translation was filled with errors, for a variety of reasons, from lazy writing, to lack of understanding due to context. I can very much see a similarity, where one would mix Russia with the Soviets, as the same as with Rome, and Byzantium; while they are similar, there are also crucial differences.