The Catholic Church (termed by you the "Church of Rome") refers to itself as "the Catholic Church" and refers to its members (members proper) as Catholics or as Catholic Christians.
From my point of view, there is no term other than "Catholic" with which the Catholics on the forum may call ourselves that is concise, accurate, and nonoffensive.
Certainly the bizarre terms of "Vatican Agent" and "Papal Submissive" as well as the clearly offensive terms of "Papist" and "Romanist" are out.
"Roman Catholic" is out because it isn't accurate - there are Eastern-Rite Catholics who are Catholic but not "Roman".
Similarly, the Orthodox shouldn't be reduced to referring to themselves as "Eastern Orthodox," as there are Orthodox who are not Eastern-Rite per se.
Of course, all of this is assuming that "catholic" and "orthodox" are simple adjectives, and don't mean the same as their capitalized counterparts.
I'm sorry that the term that Catholics (i.e. those in communion with the Pope) use to precisely reflect our Church is confusing to you. I explained the capital 'C' / lower-case 'c' manner of understanding it - that is the way that most people keep the two straight and in the world outside of FR seems to work pretty well. Beyond that, I really can't help you.
How about: Churches associated with the Roman Bishop?
I explained the capital 'C' / lower-case 'c' manner of understanding it
And I posted a known definition in which the proper name Catholic includes individuals like myself.
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Oh, Right--that is, from the perspective of
THE GRAND SUPREME AUTHORITY OF THE DOGMATIC !!!!CONTROL!!!! FREAQUES of the Vatican INTITUTION who abjectly
!!!!!DEMAND!!!!! THAT ALL TPC's [Trinitarian Protty Christians]
UTTERLY AND TOTALLY IN 100% KOWTOWING SUBMISSION AND OBEISANCE TO whatever Vatican affiliate whim of the moment demands that they do.
Where's the barf bag? What horrific heretical theology! What horrific heretical terminal arrogance!