Not in those verses, but elsewhere.
CATHOLIC means 'Universal', which in itself means, 'of or relating to, or affecting the entire world and ALL peoples therein'. It means, ALL encompassing, comprehensibly broad, general, and containing ALL that is necessary. In summation, it means ALL people in ALL places, having ALL that is necessary, and for ALL time.
in Matthew 28:19-20, "Go, therefore and make disciples of ALL nations...teaching them to observe ALL that I have commanded you; And behold, I am with you ALL days, even unto the consummation of the world."
That is a statement of Universality, Katholicos, Catholicus, Catholic.
…
.and you belong to that Church whose faith St. Paul describes as being "proclaimed (KATAnggeletai) in the whole universe (en HOLO to kosmo)” (Rom. 1:8)
Thus the word
KATAHOLOS or
Catholic in English originated from Scriptures - Romans 1:8
"So the church
throughout all Judea and Galilee and Sama'ria had peace and was built up; and walking in the fear of the Lord and in the comfort of the Holy Spirit it was multiplied." [Acts 9:31 RSV]
There the words "church throughout all" is translated from the Greek words "Ecclesia kata holis". Thus, kataholos, or Catholic in English, originated in Scripture:
Romans 1:8 and Acts 9:31
But it was after Ignatius that the term Catholic Church became used more and more to designate the true church.
"Where the Bishop appears, there let the people be, just as where Jesus Christ is, there is the Catholic Church."
St. Ignatius of Antioch's letter to the Smyrneans, paragraph 8, of 106 A.D.,
Undoubtedly the word was in use before the time of this writing. St. Ignatius was the third bishop of Antioch and thought to have been trained by St. John the Apostle. Keep in mind 106 AD is a mere 11 years after John wrote Revelation.
Other written records of the term "CATHOLIC" describing a character of the Christian Church:
Martyrdom of St. Polycarp 155AD;
Clement of Alexandria, Stromateis 202AD;
Cyprian, Unity of the Catholic Church 251AD;
Cyprian, Letter to Florentius, 254AD
"Christian is my name, and Catholic my surname. The one designates me, while the other makes me specific. Thus am I attested and set apart... When we are called Catholics it is by this appellation that our people are kept apart from any heretical name."
Saint Pacian of Barcelona, Letter to Sympronian, 375 A.D.
That's true, Peter said that. But that is not why Jesus changed his name.
W.F. Albright (Protestant) and C.S. Mann
“[Peter] is not a name, but an appellation and a play on words. There is no evidence of Peter or Kephas as a name before Christian times….Peter as Rock will be the foundation of the future community.
Jesus, not quoting the Old Testament, here uses Aramaic, not Hebrew, and so uses the only Aramaic word that would serve his purpose. In view of the background of v. 19…
one must dismiss as confessional interpretation any attempt to see this rock as meaning the faith, or the messianic confession, of Peter. To deny the pre-eminent position of Peter among the disciples or in the early Christian community
is a denial of the evidence…The interest in Peter’s failures and vacillations does not detract from this pre-eminence; rather, it emphasizes it. Had Peter been a lesser figure his behavior would have been of far less consequence.”
(The Anchor Bible; Matthew [Garden City, N.Y.: Doubleday & Co., 1971], 195)
Albert Barnes (Nineteenth-Century Presbyterian)
"The meaning of this phrase may be thus expressed: ‘Thou, in saying that I am the Son of God, hast called me by a name expressive of my true character. I, also, have given to thee a name expressive of your character. I have called you Peter, a rock. . . . I see that you are worthy of the name and will be a distinguished support of my religion"
[Barnes’ Notes on the New Testament, 170].
John Broadus (Nineteenth-Century Calvinistic Baptist)
"As Peter means rock, the natural interpretation is that ‘upon this rock’ means upon thee. . . . It is an even more far-fetched and harsh play upon words if we understand the rock to be Christ and
a very feeble and almost unmeaning play upon words if the rock is Peter’s confession"
[Commentary on the Gospel of Matthew, 356].
Craig L. Blomberg (Baptist)
"The expression ‘this rock’ almost certainly refers to Peter, following immediately after his name, just as the words following ‘the Christ’ in verse 16 applied to Jesus. The play on words in the Greek between Peter’s name (Petros) and the word ‘rock’ (petra) makes sense only if Peter is the Rock and if Jesus is about to explain the significance of this identification"
[New American Commentary: Matthew, 22:252].
