Critics of the New Testament often claim that the names of the authors of the Gospels were added after they had already been in circulation in the early Church. Instead of Matthew, Mark, Luke, and John, they say, the real authors were anonymous Christians who relied on hearsay and legend rather than eyewitness testimony.
Is there evidence for this claim?
First, it should be noted that even if the earliest copies of the Gospels did not contain the names of their authors, that would not disprove the traditional authorship of those texts. The works of the ancient Roman historian Tacitus often do not bear his name, but few historians have ever questioned that Tacitus wrote them. We know Tacitus is the author of these works because other ancient writers, like St. Jerome, identify him as the author.
St. Augustine dealt with the charge that the Gospels were anonymous in the fourth century in his reply to the heretic Faustus:
How do we know the authorship of the works of Plato, Aristotle, Cicero, Varro, and other similar writers but by the unbroken chain of evidence? So also with the numerous commentaries on the ecclesiastical books, which have no canonical authority and yet show a desire of usefulness and a spirit of inquiry. . . . How can we be sure of the authorship of any book, if we doubt the apostolic origin of those books which are attributed to the apostles by the Church which the apostles themselves founded.
Furthermore, there is no compelling evidence that the first manuscripts of the Gospels didlack attribution to their traditional authors. There are no manuscripts that simply lack titles (as lay critics might imagine). Academic critics, on the other hand, say the variants in the titles of those early manuscripts prove the author’s names were added at a much later date. However, the usual variant is just the absence of the word “Gospel" which leaves a title that begins with “According to . . ." followed by the author’s name which, by the way, is never absent from these manuscripts.
Another argument in favor of the traditional authorship of the Gospels is this: if they had been forged, it is highly likely the forgers would have pretended to be more impressive-sounding authors. This is what heretics in the second, third, and fourth centuries did when they attributed their forged Gospels to people like Peter, Philip, and even Mary Magdalene. Why pretend to be a relative unknown such as Mark or Luke? Why would they impersonate a persona non grata such as Matthew, whose popularity as a former tax collector would have been only slightly higher than that of Judas Iscariot?
Biblical scholar Brant Pitre aptly summarizes the issue: “According to the basic rules of textual criticism, then, if anything is original in the titles, it is the names of the authors. They are at least as original as any other part of the Gospels for which we have unanimous manuscript evidence."
 See the introduction to Tacitus’ Annals at the Loeb Classical Library online athttp://penelope.uchicago.edu/Thayer/E/Roman/Texts/Tacitus/Annals/Introduction
 St. Augustine. Contra Faustum, Book XXXIII.6.
 See for example Bart Ehrman, Jesus Apocalyptic Prophet of the New Millennium (New York: Oxford University Press, 1999) 248-250.
 Granted, some may use this argument to try and prove that John’s Gospel is a forgery, but the eyewitness details in that text and external sources that corroborate John’s authorship make the Fourth Gospel completely different in kind to the forgeries that came centuries later (for more see Craig Blomberg’s book The Historical Reliability of John’s Gospel).
 Brant Pitre, The Case for Jesus: The Biblical and Historical Evidence for Christ (New York: Doubleday, 2016), 17.