
Greek Orthodox was created because the Byzantines were Christians, but they did not follow Catholic faith. Therefore, they created Greek Orthodox.
The Cathedrals where the Byzantines prayed, all masses were in Greek (hence the name, Greek Orthodox). The Byzantines also hired Missionaries that translated the Bible into the language of the people they were trying to convert. Many of the people in Byzantine agreed that the patriarch, and the bishop of Constantinople dominated the Byzantine Church. The emperor appointed the Patriarch and the patriarch was superior to him. The bishops could not marry because they were supposed to be focusing on god, but the clergy and priests could marry.
Greek Orthodox is still a well-known religion today. All though Greek Orthodox is still used today, it is usually called Eastern Orthodox. Same as always, the patriarch of Constantinople is head of the Church. Except the Patriarch has no real authority over the Churches now. Overall, Greek Orthodox had a big impact on the Byzantine Empire and it is still impacting us today.