Greek Melkite Catholics?

Why are Melkite Catholics called Greek Melkite Catholics? 1) The word "Melkite" is derived from "followers of Malek" i.e followers of the emperor or king. It was used as a derogatory term by Christians who did not accept the decisions of the Council of Chalcedon (451 AD) against those Christians who accepted it. The Council declared that in Christ there are two natures human and divine distinct but united in his one person. 2) The word "Greek" refers to the Eastern Roman empire which extended its governance over all the Middle East and whose centre was Constantinople (today Istanbul) i.e. Byzantium. Its cultural language is Greek. Since the Church of Antioch was situated in this Greek/Byzantine culture, Christians who lived in Antioch were called Greek (Room) by the Arab conquerors of the 7th century. 3) Although the Church of Antioch distanced itself from the effects of the 1054 schism between the Churches of Rome and Constantinople, its geographical and cultural proximity to Constantinople slowly reflected a pressure or tendency to be Orthodox Christian. However, in 1724 bishop Cyril Tannas and other bishops in the Church of Antioch declared their communion with the Church of Rome. This decision resulted in the pope recognizing Cyril as a patriarch of Antioch in 1729 and, at the same time, some other bishops in Antioch preferring to stay in communion with Orthodox Constantinople. Since the reunion with the Roman Church, the followers of Patriarch Cyril Tannas have been part of the Catholic Church. Note that the Church of Rome recognizes the traditions of all Eastern Churches in union with her.