Well, first that song was a cover by They Might Be Giants. It first came out in 1953.

"Istanbul" had been one possible name for the city for centuries, but in 1930 Turkey passed a law making it the official name you have to use if you want the post office to deliver your mail.

As for why historians use different names, at least for the ancient world it has to do with what was common usage at the time. So if I were writing about the Peloponnesian War, I'd use Byzantium, because that's what Thucydides used. If the Byzantine Empire, Constantinople.

It's the same reason you don't find ancient historians writing about Asia Minor as Turkey unless to say something like "located in modern Turkey."