When I first discovered the history of the term "Roman Catholic", its usage bothered me. As I understand it, the communion to which I belong is the One, Holy, Catholic, and Apostolic Church. Hence, it would seem best to refer the the Church as just "Catholic".
However, my interaction with Byzantine and other Eastern Catholics modified my view. Since not all of them practice the traditions of Rome, I have felt, at times, that it would be appropriate to refer to the "Latin Church" either as Latins or Romans, and the other Churches by their specific names, such as the "Ruthenian Catholic Church".
My interaction with Eastern Orthodox Christians has modified my view further. Ridiculous debates, debates in which I have participated willfully, have lead me to believe that the whole discussion over names is simply pointless. There are those who, no matter what, will call catholics "papists" or who will refer to the Catholic Church as "The Vatican" (which is nothing but nonsense born of prejudice). However, I choose not to further particapte in games with those whose only goal in life is to express biggotry against Christ's Bride. So call us "Catholics;" call us "Romanists;" call us whatever you please. It matters little to those who believe that the churches in communion with Rome form the One, Holy, Catholic, and Apostolic Church founded by Jesus Christ.
Battles about what we call ourselves and what some outside our communion call us, do little to save souls.