It is true that Ethiopia was never conquered, and the only exception to that would be the temporary occupation by the Italians in WWII. Also, there are not large chunks of ethiopian history missing. I know a lot about Ethiopia's history, at least from the first millenium to the present, and the only part of history that is not yet well known of ethiopia is the time before the 1st millenium. Also, this is only because archaelogy has not existed in Ethiopia for a long enough time, as in egypt, for much if its ancient history to be uncovered. Even recently, archaelogists have found more and more ancient artifacts in Ethiopia. In fact, they found a piece of "teff" (one of the first grains ever to be cultivated that is not found outside of Ethiopia) in an ancient Egyptian mud brick once.
As for the name Ethiopia, it is true that it was often used to describe all of black Africa, as well as Ethiopia itself, but if Ethiopia is the remaining civ, its name should rest as Ethiopia, and not as Abyssinia or Axum. Abyssinia is a newer name for Ethiopia and was used to denote the northern area of Ethiopia. Also, Axum was more of a dynasty, and to name the civ Axum would be like naming the Chinese civ Zhou.
As for the actual region that "Ethiopia" denotes, Ethiopia was not simply used to determine black africa. More accurately, Herodetus used it to describe Nubia, Ethiopia, and India, as the three ancient states had similar features. Ethiopia, however, was refered to the bible, and you cannot dismiss all references to Ethiopia as being about other places. Even if Ethiopia wasn't an accurate term to describe the nation today, Ethiopia as a civilization was still important and should be recognized by Sid, and put in as a civ in conquests under the name Ethiopia.
Sorry for the long rant, but I just had to clear some stuff up.
Edit: What neighboring barbarians are you speaking of? If you mean the war against Ahmad Gran in 1541, somalia was often a part of Ethiopia and Ethiopia ultimately won that war. Could you clarify when and by whom Ethiopia was conquered?