There are four canonical Gospels... The Gospel of Mark, Gospel of Matthew, Gospel of Luke and Gospel of John, written during 70 to 100 CE. I have always taken it for granted that these books were written by individiuals named Mark, Matthew, Luke and John. Why would I ever think otherwise? Many people agree with my assumption, including many scholars and theologians.
John A. Tvedtness, resident scholar at the Institute for the Study and Preservation of Ancient Religious Texts at Brigham Young University confirms that the author of the Gospel of Matthew was the apostle Levi Matthew and that the author of the Gospel of John was the apostle John. These were the only two of the Gospel writers who knew Jesus personally. (Matthew 4:21; 9:9)
Tvedtness also confirms that the Gospel of Mark was written by an evangelist named John, whose Latin name was Marcus, generally known as Mark. Mark is said to have been the nephew of Mary, the sister of Barnabas (Act 12:12; Colossians 4:10), which would explain why he accompanied Barnabas and his friend Paul on missionary journeys (Acts 12:25; 15:36-40; 2 Timothy 4:11). He later traveled with the apostle Peter, who called the young man "my son" (1 Peter 5:13)).
Several early Christian writers indicated that Mark's gospel comprised a collection of stories about Jesus that he heard from Peter. Barnabas, a native of Cyprus, was an early convert to the church (Acts 4:36), but there is no indication that either he or his nephew Mark had known Jesus.
Luke (or Lucas), was a physician by trade and was one of Paul's later missionary companions (Colossians 4:14; 2 Timothy 4:11; Philemon 1:24). Some believe that Luke was Paul's physician. In the view of Tvedtness and others, Luke is the author of both the gospel that bears his name and the Acts of the Apostles (compare Luke 1:1-4 with Acts 1:1 and note the use of Awe in Acts 16:10-13, 16; 20:6, 13-15; 21:1-8, 10, 12, 14-17; 27:1-5, 7, 15-16, 18-20, 26-27, 29, 37; 28:10-14, 16). Luke was at least a second-generation Christian and had not known Jesus.
If you only go by the views of scholars such as Tvedtness (and many do), you would assume that the identify of the Gospel writers is a simple fact of history. It is interesting to note that this is not the case.
Randel Helms, professor and biblical scholar at Arizona State University, is the author of a book titled "Who Wrote the Gospels?".
According to Helms, the names we associate with the Gospel writers are all "second-century guesses". The authors of the four Gospels never explicitly identified themselves. The indication is that the Gospels were written anonymously and that the names Mark, Matthew, Luke and John were later assigned.
Nearly a century after the four Gospels were written, Christians in the late-second century, eager to give names to the anonymous manuscripts they possessed, selected traditional figures that they supposed should have written them--the apostles Matthew and John, Luke the "beloved physician" of Paul (Colossians 4:14), and John Mark of Jerusalem, the "son" of Peter (Acts 12:12; 1 Peter 5:13).
Helms states that the Gospels were written to confirm or convert their readers to Christianity, that they are the highly colored arguments of powerful authors, not just transparent windows upon the historical Jesus.
Others believe that while is it possible that Matthew, Mark, and Luke could have written their respective Gospels themselves, it is perhaps equally if not more probable that these Gospels were written by some student/companion of these important early Christians. It was customary in early times for a relatively unknown person to give to his or her written work the name of a well-known figure in order for it to have more authority and ensure that it would be read.
John's Gospel is more complex: its early redactions may have come from John himself, but the final redaction which we have today may well be the result of a disciple of John finalizing the text.