John’s gospel never really seriously questioned or disputed until after the reformation.
What was questioned was the book of Revelation, repeatedly, because of the supposed different writing styles. Some thought this was a different John.
Not sure why he chose to not be more direct about himself. Keep in mind he was in the company of the most humble woman to ever exist, our Lady (John 19:27), so maybe this had a effect on him overall? Jesus spoke often of humility (the last will be first, sit at the end of the table, not the front etc) And it is my personal belief that this is why his gospel account differs so much from the synoptics. He was in the company of the mother of God, the one who had the encounter with the angel Gabriel and the Holy Spirit. She knew who Her Son was and I believe she relayed this very clearly to John(just reaffirmed, not that he didnt already know)…so when we open up his gospel we see from the very beginning he is informing the reader that Jesus is 2nd person of the Godhead. That’s my personal opinion, anyway…
Don’t know of anything official or authoritative, but his followers spoke of him/the fourth gospel. From New Advent:
The evidence given by the early ecclesiastical authors, whose reference to questions of authorship is but incidental, agrees with that of the above mentioned sources. St. Dionysius of Alexandria (264-5), it is true, sought for a different author for the Apocalypse, owing to the special difficulties which were being then urged by the Millennarianists in Egypt; but he always took for granted as an undoubted fact that the Apostle John was the author of the Fourth Gospel. Equally clear is the testimony of Origen (d. 254). He knew from the tradition of the Church that John was the last of the Evangelists to compose his Gospel (Eusebius, Church History VI.25.6), and at least a great portion of his commentary on the Gospel of St. John, in which he everywhere makes clear his conviction of the Apostolic origin of the work has come down to us. Origen’s teacher, Clement of Alexandria (d. before 215-6), relates as “the tradition of the old presbyters”, that the Apostle John, the last of the Evangelists, “filled with the Holy Ghost, had written a spiritual Gospel” (Eusebius, op. cit., VI, xiv, 7).
Of still greater importance is the testimony of St. Irenæus, Bishop of Lyons (d. about 202), linked immediately with the Apostolic Age as he is, through his teacher Polycarp, the disciple of the Apostle John. The native country of Irenaeus (Asia Minor) and the scene of his subsequent ministry (Gaul) render him a witness of the Faith in both the Eastern and the Western Church. He cites in his writings at least one hundred verses from the Fourth Gospel, often with the remark, “as John, the disciple of the Lord, says”. In speaking of the composition of the Four Gospels, he says of the last: “Later John, the disciple of the Lord who rested on His breast, also wrote a Gospel, while he was residing at Ephesus in Asia” (Adv. Haer., III, i, n. 2). As here, so also in the other texts it is clear that by “John, the disciple of the Lord,” he means none other than the Apostle John.
We find that the same conviction concerning the authorship of the Fourth Gospel is expressed at greater length in the Roman Church, about 170, by the writer of the Muratorian Fragment (lines 9-34). Bishop Theophilus of Antioch in Syria (before 181) also cites the beginning of the Fourth Gospel as the words of John (Ad Autolycum, II, xxii). Finally, according to the testimony of a Vatican manuscript (Codex Regin Sueci seu Alexandrinus, 14), Bishop Papias of Hierapolis in Phrygia, an immediate disciple of the Apostle John, included in his great exegetical work an account of the composition of the Gospel by St. John during which he had been employed as scribe by the Apostle.