Lets do this in steps...
1. Either the Pope is forced to leave Rome in one of the gazillion times the city got sacked between 476 and 1944...or after the Roman Empire becomes Christian, the Emperor calls it the Roman Christian Church or something like that...Roman Empire collapses and with it, the justification of calling it Roman...I guess the Pope might move to Constantinople...
2. Catholic...Hmmm...since it means universal in Latin...easy enough, well not really, but lets say they become a minority religion in Europe...bigger reformation+worse leadership for Rome+something else...Catholicism becomes a minority religion...or...they split between west and east leaves the catholics as the small religion...
3. Not a church...now that's hard! how about a small religion without a large organization...is there a Jewish Church? I don't know, but let's say there's a Christian diaspora in the times of the Roman Empire and there's no church (I think there were like 7 Christian churches before the centralization at Rome, not sure)...just a religion...like the Jews pre-1948, or they worked differently?