How did the Byzantine empire become an empire

‘Byzantine empire’ is a word used to describe the eastern portion of the Roman Empire that existed until the fall of it’s capital Constantinople to the Ottoman Turks in 1453. Hence it was always an empire as it’s name is used in modern scholarship to differentiate the Vestigial eastern remnant from the earlier and better known western half of the roman Empire, which despite debate essentially seeced to exist as a Roman political entity in 476 with he dispossession of Romulus Augustulus (the last Roman Emperor) from power.