The term "Roman Catholic" became common only after the East/West separation of the Church in 1054 AD. It was further reinforced in the West after Martin Luther’s protest in the sixteenth century.
There is good reason to oppose many things linked to the Roman Empire. The New Testament’s book of Revelation speaks of Rome as “Babylon” and “the mother of whores” (see 17:5). The Church steadfastly resisted the claim to the title “God and Lord” by the Emperor Domitian and his readiness to brand as atheists those who rejected the official state religion.
There were already Christians in Rome when the apostles Peter and Paul arrived to strengthen that faith community. In that city they were martyred and are buried. Very different in temperament and background, they evangelized Jews and gentiles respectively. The fact that they share a single feast (June 29) suggests that the Church has long recognized legitimate diversity of thought and action. At times, however, the Church must designate some ideas and practices as incompatible with the Good News of Jesus Christ.
We should remember that the oldest term in Scripture for Jesus’ disciples is “followers of the Way” (Acts 9:2). It was in Antioch that they were first called “Christians” (see Acts 11:26). The author of Acts of the Apostles ends his story with St. Paul’s ministry in Rome. From that city, the Good News of Jesus would spread to the rest of the known world.