As an amateur historian I’ve stopped and urge other people to stop using the term Byzantine empire.
It was the Roman empire. They called and considered themselves Roman. The European, Arab, Iranian and Turkic powers called them the Roman empire.
It was only Gibbons with his extremely flawed and inaccurate book and the Germanic historians of his time in the 18th century who called it “the Byzantine empire “.
For really understanding it we must call and consider it the continuation of the Roman empire of Cincinnatus, Caesar, Cicero, Caligula and Caracalla
To a minor degree I accept your argument, primarily because the Moscow Patriarchate has called itself “The Third Rome” or, more boldly, “The New Rome”.
Great to know. Looks like our education system has been manipulated even when we were in school.
Now it seems the evidence is piling up that the dating of the Egyptian era is wrong. Fascinating times.