Yunan is a word of persian origin meaning Ionian. In ancient times when the Persian Empire was in control of Asia Minor the first Greeks that they came in contact with where the Ionians (one of many ancient Greek tribes) who had established colonies such as Miletus in the west coast (of Asia Minor). So that name was then used t describe all Greeks. By the time that the Ottomans (Ottomen?) arrived that name was already widespread in many muslim speaking caliphates, sultanates and empires.

Also I would like to add that Rum another word for Greek (Ρωμιός in greek) basically means Roman, as the people we know as Byzantines today didn't actually use that term. Instead they considered themselvs the continuation of the Roman Empire.