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Until Herakleios I (early 600s) the Latin titles were used. He replaced them with Basileus. Later ones added or subtracted things such as Sebastokrator etc.
The term Byzantine was invented by the humanist Hieronymus Wolf (17.c.) and spread out by Montesquieu. The empire and people always referred to themselves as Romans (Romaioi). Constantinopolis was not Byzantion/Byzantium, it was built on top of it, on third times the land, by the name "New Rome".
(Still today, the Ecumenic Orthodox Patriarch of Istanbul is officially addressed as Archbishop of Constantinople, New Rome, the Ecumenic Patriarch.)
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