I read somewhere that the byzantines never stopped calling themselves romans. Also a few of their enemies called them romans. Like the turks. I think it was the Europeans who started calling them byzantines to mock them since there was quite a bit of friction between the east and the western churches. Since European historians wrote most of modern history, the name carried. I was reading Edward Gibbon's Decline Ans Fall, and in that book, he spends most of the end of the book insulting byzantines, especially Alexius. He reffered to them as the Barbarians.