"Are you saying that Orthodox or Orthodox Christian is not how you would refer to your church had Rome not arrogated to itself the term Catholic Church?"
The quick answer is "sort of". Prior to the Great Schism, the Fathers always referred to The Church as simply "The Church" or "The Catholic Church" or earlier, the "catholic church". All of the Fathers also referred to the Faith as the "orthodox faith", or spoke of "orthodoxy". Since the Schism, the West has used "Catholic", the East generally but not always "Orthodox", but we both still say that we believe in "one, holy, catholic and apostolic church" in conformity with the Creed the Fathers established at Nicea.