And who was the man to coin this term?
The term Byzantine was coined about 100 years after the fall of Constantinople by historians who wanted to differentiate the empire that continued in Greek form from its roots in the Roman Empire. The name derives from the Greek city Byzantium which was chosen as the site for Nova Roma (New Rome) by Constantine. The citizens chose to call the city Constantinople instead of Nova Roma. The "Byzantines" themselves continued to refer to themselves as Romans. To this day the Turks still refer to Greeks as "Rum" (Romans). The empire was never referred to as Byzantine before the fall of Constantinople to the Turks in 1453.