Imperium Romanum. In Republican Roman law, Imperium referred to the authority of an official over a specific thing (like a province). When the Imperial era began, the emperors were given Imperium over the whole empire, which is where the English words for "empire" and "emperor" come from. So Imperium Romanum can be literally interpreted as the area under Roman jurisdiction.

When the Empire's official language became Greek in 610, the name they used to refer to the place was Basileia Rhomaion which is pretty roughly translated as: "Roman Kingdom".