Classic Catholic

A rose by any other name....
St. Athanasius, in his Orations Agains the Arians uses any and every argument he can think of to counter the Arian threat. In Book I, 2, he uses the argument that Arius must be a heretic because his disciples are named after him. So, they are "Arians," not Christians. Athanasius uses the Marcionites and other heretics as parallel examples.

I've heard similar arguments made re: Lutherans. An analogous argument might be made concerning "Anglicans." I'm wondering, though, what one does with the Catholic insistance on being in communion with Rome and being, in a sense, a Petrine Church, especially in light of St. Paul's discussion in I Cor. 1:12 about saying "I belong to Kephas." Of course, we didn't come up with the name "Roman Catholic." I think Protestants came up with that for us. We prefer just plain "Catholic," and have traditionally preferred "Orthodox" as well, although since 1054 we don't use that as much.

Any thoughts?