Well we’ve had Rome, Eastern Rome, Holy Rome, Imperial Russia, Imperial Spain, fascist Italy, Nazi Germany, Greece, all of which claimed to be the continuation of Rome, so I think this would be the 8th or 9th Rome.

Don't forget Ottoman Turkey, one of titles of Sultan since Mehmed II was Kayser-i Rum which literally mean "Roman Emperor" and this was even acknowledged by some treaties with Italians and even German Emperors.