"But, under the Apostles, you will say, "no one was called a Catholic".
Grant this to have been the fact; or suppose it to have been so.

• When heresies, after the Apostles days, arose, and, under diverse names, strove to tear and scatter piecemeal the dove of God, and His queen, did not the Apostolic people require a peculiar name, whereby to distinguish the unity of the people that had not been corrupted, for fear lest the error of a few might tear limb by limb the unstained virgin of God?
• Was it not beseeming that the principal head should be designated by a suitable title?

Suppose I entered, this very day, into a populous city, and found there Marcionites, Apollinarists, Cataphrygians, Novatians, and others of the same sort, all calling themselves Christians.

• By what name should I be able to recognize the congregation of my own people, were it not from its being called Catholic?

Come, tell me, you who bestowed so many names on the other peoples!

• Why have so many cities, so many nations, each having their own description?
• The very man who calls in question the name Catholic, will he be ignorant of the cause of his own name, if I shall inquire its origin?
• Whence was it delivered to me?

Assuredly, that which has stood during so many ages was not borrowed from man.

This name Catholic sounds not of Marcion, nor of Apelles, nor of Montanus, nor does it take heretics as its authors. . . . . Christian is my name, but Catholic my surname. That names me, this describes me; by this I am approved; by that designated. And if at last we must give an account of the word Catholic, and express it, from the Greek, by a Latin interpretation, Catholic is "everywhere one", or, as the more learned think, obedience in all the commandments of God. . . . Therefore he who is a Catholic, the same is obedient to what is right. He who is obedient, the same is a Christian, and thus the Catholic is a Christian.

Wherefore when our people are named Catholic, they are separated by this appellation from the [other] heretical names.

St. Pacian of Barcelona, (c.310-375 A.D.), bishop of Barcelona, Jerome praises his eloquence, learning, chastity, and holiness of life.

Paraphrasing from the Catechism: The word Catholic means universal, in the sense that it is the Christian Faith according to its totality or in keeping with the whole.
The Church is Catholic in a double sense:

First, the Church is Catholic because Christ is present in her.

"Where there is Christ Jesus, there is the Catholic Church."
— St. Ignatius of Antioch, In 107 A.D.

From the Catechism: In her subsists the fullness of Christ's body united with its head; this implies that she receives from Him the fullness of the means of salvation which He has willed: correct and complete confession of faith, full sacramental life, and ordained ministry in apostolic succession. The Church was, in this fundamental sense, Catholic on the day of Pentecost and will always be so until the day of the Parousia.