Take Egypt. The ancient Egyptian name of the country is Kemet, and the modern Arabic name of the country is Misr (or Masr), a word with Semitic origin. Egypt comes from the the Latin Aegyptus, which in turn derives from the ancient Greek Aígyptos, which means “below the Aegean [Sea]”.
Then in the Caucasus, ethnic Georgians call themselves Kartvelebi, their land Sakartvelo, and their languageKartuli. Georgia comes from a belief that came back to Medieval Europe from the Crusades that the country is the home of St. George, a Roman Christian martyr. And in Armenia, the native name for the country is Hayk, which in the Middle Ages was extended to Hayastan, by addition of the Iranian suffix -stan (land). The name Armenia derives from old Persian and Ancient Greek.Basically, we're using the names of dead empires in dead languages to describe whatever roughly exists in the same geographic area today...who cares what ethnic groups call their own homeland?
Interesting side note: the English language also inherited describing geographic south as "down" from the Greeks and Romans - because if Egypt were really underneath the Aegean Sea, it certainly wouldn't be a country today.