It became known as the Byzantine Empire in the mid-1500s by way of a German historian, who wrote about them a century after the city had fallen to the Turks. Byzantium was the name of the city before Emperor Constantine made it the new capital of the Roman Empire and it was subsequently renamed Constantinople.

So why not the Constantinople Empire? Largely because it never ceased to be the (Eastern) Roman Empire in the first place. It was culturally Greek rather than Latin, but it was still more or less the same political entity until it feel in 1453, and they still certainly considered themselves Romans even if they used the Greek Rhomaioi rather than the Latin Romani.

So, to answer your question, it is called the Byzantine Empire because a German historian, arguably incorrectly, called them Byzantines. The "Byzantines" never ceased to consider themselves as Romans. Using the term Roman Empire (or Eastern Roman Empire) to describe them would be correct, but I personally feel that Byzantine Empire is serves a purpose as it specifically refers to the Eastern Roman Empire after the fall of its western counterpart.

The Eastern Emperor was occasionaly called Imperator Constantinopolitanus by western writers, if only out of spite. I'm guessing that byzantine was a way to put them down even more.