What I'm wondering is whether the actual authors of the book of John, Luke, Matthew, and Mark are who we believe them to be. I go to a Catholic high school, and in our version of the Bible it says, in the author section for each gospel, something like "traditionally the apostle John", so does that mean it could have been someone else, and we just say that the author was John the Apostle when it wasn't?
I will start a little off-topic as it is relevant to do so.
An answer to this question would not have been easy if there was no early persecution of Christianity. It would have been a lot easier for detractors of Christianity to make a point that all the writings that we have today on which the foundation of Christianity is based upon, were in fact all cooked up and doctored with the help of the political and reigning powers at that time. But the fact is, all the worldly forces were trying to wipe out nascent Christianity by persecution and destroying all their literature. All that we have today has passed through a most turbulent period and has survived under most cruel persecution. By the time Christians could live a serene living under a favourable reigning emperor, all present day Gospels were already in use , as independent books before they were canonised in this favourable time.
To answer the question: We don’t have the original documents in our possession of any of the Gospels, thanks to this persecution. Agnostics raise this point in casting doubt on the authorship of Bible books. But seen from the table below it can be said of any other ancient literature on the surface of this earth and that too with no attempts of supression. That is the case with every historical writings and we find that evidence for authenticity of Gospel writers is much stronger than any of the other historical books.
Apart from this shortest timeline for the earliest copy, there are other numerous external written sources, which are but only positive indicators (and absolutely nothing negative) in early history, that the gospels were written by the persons to whom they were attributed by the early church (Matthew, Mark, Luke and John).
A point to note: The two of the gospels are ascribed to such minor characters as Mark and Luke -- neither of whom, by any accounts, were themselves neither disciples nor the eyewitnesses is solid indirect clue they were who they were. If early Christian evangelist wanted to acquire credibility for what they were writing (or forging as some claim) and preaching they would undoubtedly have attributed it to someone like Peter, Thomas or James. And precisely this was what the later second and third century Gnostic gospels did. At least Christians are saying that all the Gospels were written under the guidance of Holy Spirit and not claiming that they were handed down by God Himself or were found buried somewhere in the ground. Or to think extremely they did not concise all the four gospels in to one book and say that it was written or dictated by Jesus himself.
This link cites the compelling evidence where it is explained in detail.
Additionally further information for Gospel of Mark is found in this link and Similar readings can be found here for Gospel of Luke and another link for Gospel of Mathew
There is much debate about the authorship of Mathew, Mark, Luke and John as well as whether they copied portions of each other’s works to form their own. Some think some or all had other common sources, etc. The reason why there is so much recent debate is unclear. For whatever reason the ‘similarities and differences’ between the gospels seem to appeal to the curiosity of men. People trying to publish a book or for whatever reason ‘invent puzzles’ on pure speculation that do not actually have any practical outcome beyond their own career and academia interest. By building ‘supposition upon supposition’ and with ‘reference upon reference’ one can build an impressive superstructure of study and scholarship. However these massive works and complex mazes can’t create anything above conjecture and for practical purposes are simply a tiring of the mind.
The simple fact of history is that we obtain less and less ability to determine what has happened in the past, the farther we move away from the event. In other words those who first identified author’s of the Bible are almost always in a better position to actually determine it. In some ways the whole subject does not matter, as it was the Holy Spirit who used men, inspired their thoughts to be infallible, had them write it down, and then move the church to accept them into a cannon of God’s word. Who were exactly involved, if they were directly written by Apostles, or only accepted by them? These and many other questions have no consequence. If authors used oral traditions, or miscellaneous histories that the Holy Spirit used and extracted portions of to fill out a divine and perfect guidance of the events, is inconsequential. God is the author. The human author does not need to be known from the biblical standpoint, nor does any possible sources that they used have any measurable value.
From a historical perspective many Bible scholars simply believe the most reliable account of the human authors are simply the traditional view upon which they were accepted into the canon by those most familiar with the subject: The Apostle Mathew wrote ‘Mathew’ while the interpreter of the Apostle Peter, whose name was Mark, wrote Mark. The historian and companion of the Apostle Paul whose name was Luke, wrote Luke, while John was written by John the Apostle. Mathew, Mark, Luke and John wrote them, as their titles bear in our bible.
There are a number of theories about who wrote the gospels. Tradition ascribes them respectively to Matthew, one of the 12 Apostles; Mark, the interpreter for Peter in Rome; Luke, a disciple of Paul; and John, one of the 12 Apostles.
Many modern scholars have doubted these attributions, primarily because the names were not attached to the gospels until many decades after they were written, but also because the descriptions the early Christians gave of the gospels do not always match the gospels we have in the New Testament. Some scholars have gone so far as to say that we can never know who wrote the gospels.
However, there is a middle ground between blindly accepting tradition and blindly rejecting tradition. First, we need to understand the changing definition of "authorship".
Ancient notions of authorship
Scholars have identified five distinct types of authorship in the ancient world.
Of the five types of authorship recognized by the ancients, only #1 and #2 would be considered authorship today (and possibly #3 if the scribe is a ghostwriter). But in ancient times most people could not write, so #1 was the least common form of authorship.
For example, Paul's letter to the Colossians begins with the heading, "Paul, an apostle of Christ Jesus by the will of God, and Timothy our brother, To the saints and faithful brothers and sisters in Christ in Colossae." It's possible that Paul dictated the letter to Timothy, but given the stylistic differences between this and other Pauline letters, it's equally possible that Timothy composed Colossians himself after consulting with Paul. In this case Paul would still be considered an author according to the customs of the time, but would not be considered the author by today's standards.
None of our four gospels contain their authors' names in the text; however, in the second century a number of other gospels began to appear, claiming to have been written by Apostles (Gospel of Thomas, Gospel of Peter or a brother of Jesus (Infancy Gospel of James). The way to gain authority for a forgery is to attribute it to a famous person and hope no one sees through the ruse.
It therefore became important for church leaders to determine which gospels were truly written by Jesus' followers and which were forgeries. It was in this context that Bishop Irenaeus gave us the names Matthew, Mark, Luke, and John. But how can we know if he was right?
Mark and Luke
Mark and Luke are relatively unknown people. Mark is mentioned in 1 Peter 5:13, and Luke in Colossians 4:14, but we have very little information about them. A later tradition claims this Mark is the same person as John Mark mentioned in Acts, but we can't know for certain. It would therefore be hard to explain how these gospels got these names if Mark and Luke were not in fact the authors.
Still, Mark is said to have composed his gospel based on the preaching of Peter, Luke on the preaching of Paul; and those are the two biggest names of early Christianity.
Modern scholars have therefore questioned this attribution. As evidence against the traditional authorship, scholars have noted that Mark appears to have drawn from a number of different oral traditions rather than from a coherent collection of sermons, and that Luke disagrees with Paul concerning events of Paul's life (e.g. Paul's trip to Jerusalem, Acts 15 vs Galatians 2). But defenders of the traditional view don't see these as major problems.
The evidence against Matthew and John as authors (in the #1 sense above) is stronger, but there is still reason to believe that these men had a hand in the books that bear their names.
Tradition tells us "Matthew put together the oracles [of the Lord] in the Hebrew language, and each one interpreted them as best he could," but the Gospel of Matthew that appears in the New Testament was almost certainly written in Greek. It's possible that the canonical Gospel of Matthew was a blend of Mark's gospel and a translation of the oracles put together by Matthew.
This would fit authorship type #4 above, and explain the discrepancies we see between the existing gospel and tradition. But we can't know for certain.
The fourth gospel comes the closest to naming an author, "the disciple who Jesus loved." However, the book shows signs of having been edited. Chapters 5 and 6, for example, appear to have been swapped from the original chronology.
Furthermore, the end of chapter 20 appears to be a conclusion to the book, with Thomas' dramatic confession, "My lord and my God!" followed by the summary, "Now Jesus did many other signs in the presence of his disciples, which are not written in this book. But these are written so that you may come to believe that Jesus is the Messiah, the Son of God, and that through believing you may have life in his name."
John 21 was thus likely added by a later writer. Verse 24 draws an explicit distinction between the author of the original book and the writer(s) of this epilogue. "This is the disciple who is testifying to these things and has written them, and we know that his testimony is true." [emphasis mine]
So while John the Apostle may have been the original author of this gospel, the final published work was likely a group effort by him and one or more of his disciples.
This would fit authorship type #3 above, and explain some of the quirks of this gospel. But again, we can't know for certain.