As we all know, Anatolia, AKA Asian Turkey, was culturally Greek for a large part of history. What would it take for Anatolia to remain Hellenized?
Hellenized, in this sense, means the following
:The people seeing themselves 'Greek'
:Greek or Latin names for places in Anatolia
:at the least 50% Christian. Denomination does not matter, as long as it is Christian.
Optional: Greece and Turkey as one country. It may be Byzantium, Greece, or any other country that can possibly acieve said requirements
If you need to alter the surrounding areas to achieve this, you may.