Source: Epistle to the Magnesians (St. Ignatius)

Let us not, therefore, be insensible to His kindness. For were He to reward us according to our works, we should cease to be. For “if Thou, Lord, shalt mark iniquities, O Lord, who shall stand?” Let us therefore prove ourselves worthy of that name which we have received. For whosoever is called by any other name besides this, he is not of God; for he has not received the prophecy which speaks thus concerning us: “The people shall be called by a new name, which the Lord shall name them, and shall be a holy people.” This was first fulfilled in Syria; for “the disciples were called Christians at Antioch,” when Paul and Peter were laying the foundations of the Church. Lay aside, therefore, the evil, the old, the corrupt leaven, and be ye changed into the new leaven of grace. Abide in Christ, that the stranger Or, “enemy.” may not have dominion over you. It is absurd to speak of Jesus Christ with the tongue, and to cherish in the mind a Judaism which has now come to an end. For where there is Christianity there cannot be Judaism. For Christ is one, in whom every nation that believes, and every tongue that confesses, is gathered unto God. And those that were of a stony heart have become the children of Abraham, the friend of God; Some read, “children of God, friends of Abraham.” and in his seed all those have been blessed who were ordained to eternal life in Christ.

BALTIMORE CATECHISM

Q. 500. Why are Catholics called "Roman"?

A. Catholics are called Roman to show that they are in union with the true Church founded by Christ and governed by the Apostles under the direction of St. Peter, by divine appointment the Chief of the Apostles, who founded the Church of Rome and was its first bishop.