" No the Catholic Church, Latin Rite."
Actually, I think that's a much better way to refer to the Church of Rome, but it has been my understanding that the Latin Rite Church has always (or for at least a real long time) called itself the Roman Catholic Church and of late has refered to itself as a particular Church within The Church. As I said, I like "Latin Rite" as it is certainly a more accurate descriptor.
I also have always liked the idea of calling the Bishop of Rome the Patriarch of the West, or the Latin Patriarch of the West, but assumed you guys would find that offensive.