Saint Pacian (310—391 AD), bishop of Barcelona and Church Father in his Epistle I explains that "Catholic" marks the unity of the people that were uncorrupted:
But under the Apostles, you will say, no one was called Catholic. Be it thus. It shall have been so. Allow even that. When after the Apostles heresies had burst forth, and were striving under various names to tear piecemeal and divide the Dove and the Queen of God, did not the Apostolic people require a name of their own, whereby to mark the unity of the people that were uncorrupted, lest the error of some should rend limb by limb the undefiled virgin of God? Was it not seemly that the chief head should be distinguished by its own peculiar appellation? Suppose, this very day, I entered a populous city. When I had found Marcionites, Apollinarians, Cataphrygians, Novatians, and others of the kind who call themselves Christians, by what name should I recognise the congregation of my own people, unless it were named Catholic? Come tell me, who bestowed so many names on the other peoples? Why have so many cities, so many nations, each their own description? The man who asks the meaning of the Catholic Name, will he be ignorant himself of the cause of his own name if I shall enquire its origin? Whence was it delivered to me? Certainly that which has stood through 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.
Many things the Holy Spirit hath taught us, Whom God sent from Heaven to the Apostles as their Comforter and Guide. Many things reason teaches us, as Paul saith, and honesty, and, as he says, nature herself. What! Is the authority of Apostolic men, of Primitive Priests, of the most blessed Martyr and Doctor Cyprian, of slight weight with us? Do we wish to teach the teacher? Are we wiser than he was, and are we puffed up by the spirit of the flesh against the man, whom his noble shedding of blood, and a crown of most glorious suffering, have set forth as a witness of the Eternal God? What thinkest thou of so many Priests on this same side, who throughout the whole world were compacted together in one bond of peace with this same Cyprian? What of so many aged Bishops, so many Martyrs, so many Confessors? Come say, if they were not sufficient authorities for the use of this name, are we sufficient for its rejection? And shall the Fathers rather follow our authority, and the antiquity of Saints give way to be emended by us, and times now putrifying through their sins, pluck out the grey hairs of Apostolic age? And yet, my brother, be not troubled; Christian is my name, but Catholic my surname. The former gives me a name, the latter distinguishes me. By the one I am approved; by the other I am but marked.
And if at last we must give an account of the word Catholic, and draw it out from the Greek by a Latin interpretation, "Catholic" is 'every where one, or, (as learned men think,) "obedience in all," i. e. all the commands of God. Whence the Apostle, Whether ye he obedient in all things; and again, For as by one man's disobedience many were made sinners, so by the obedience of One shall many be made righteous. Therefore he who is a Catholic, the same man is obedient . He who is obedient, the same is a Christian, and thus the Catholic is a Christian. Wherefore our people when named Catholic are separated by this appellation from the heretical name. But if also the word Catholic means 'every where one,' as those first think, David indicates this very thing, when he saith, The queen did stand in a vesture of gold, wrought about with, divers colours; that is, one amidst all. And in the Song of Songs the Bridegroom speaketh these words, My dove, My undefiled, is but one; she is the only one of her mother; she is the choice one of her that bare her. Again it is written, The virgins shall be brought unto the King after her. And further, Virgins without number. Therefore amidst all she is one, and one over all. If thou askest the reason of the name, it is evident.