Epithets for Makedonian Kings

[machinor]

The triumphal cognomen like Asiaticus, Africanus, Germanicus etc. were an exclusively Roman thing AFAIK. Hellenistic monarchs did also have cognomen. At first those were given to them by their people or armies like Antiochos I Soter ("Saviour") for saving Asia Minor from the Galatians or Seleukos I Nikator ("The Victorious") well for being victorious. Later on however they began to choose their cognomen for themselves as part of their self-image that they wanted to propagate; the first one to do this was Antiochos IV called Epiphanes ("The Manifest" or "The Illustrious") or sometimes also Theos Epiphanes ("God Manifest"). That's at least how it was in the Seleukid Dynasty. Don't know about the others though but the about the same process from typical nicknames given because of triumphal deeds or distinctive features by their troops and peoples to self-chosen propagandistic "throne name", if you will.

Asiatikos or Rhodios would mean "from Asia" and "from Rhodos", so I would not use those kind of cognomen. Hellenistic kings wouldn't degrade themselves to adopt Roman *spits out* naming customs anyway. ;)

EDIT: If you want to name them "Conqueror of Asia" or something like that you'd have to form the according compound noun. My knowledge of Ancient Greek grammar is to vague to give you any instruction on that, though. Could be something like "Asiorketes" or "Nikasiatikos" or something like that. That's just a wild guess though.