Putin considers himself to be the repristinization of the Byzantine Emperor.
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