I know that the Byzantines called themselves "Roman", but what did other peoples, such as the Venetians, call them at the time?
In addition to the other link, which refers to what Europeans called them, the Arabs also referred them as the Romans, "ar-Rum". There's even an entire sura of the Quran entitled ar-Rum. Down to today, there's an expression among the Arab Greek Orthodox that "God is Roman", meaning Orthodox, not Catholic.
As you might imagine this has been asked before. I specifically liked this response from /u/Ambarenya discussing the First Crusade. Basically people called the Byzantine Empire Rome.