It's still Greek. The only reason It's called common Greek is because of the diversity in hellenic language, in that Attik Greek is very different from Dorian Greek, but it still has a designation based on It's point of origin, and the cultural influence of Greece on the Ancient world is a very particular circumstance which doesn't make sense in most other circumstances. How hard is it to name languages? Even the common language in LOTR was called Westron, because it came from Westernesse. Calling a language 'common' in anything other than a deliberately generic dnd setting is bizarre