I could probably write on this topic for quite some time because I find it endlessly fascinating, but my wife has informed me that I have gone a bit off the rails at this point, so let me bring this series on gospel authorship (Parts I, II, III, IV, V, VI) to a close with one final post in which I set forth a more or less mainstream scholarly narrative reconstruction of gospel authorship as I see it.
Jesus was crucified by the Romans around the year 30 C.E. If any narrative of Jesus' life was written in the 30 or so years after his death, those writings have not survived. Yet, the message about Jesus was passed orally from person to person, from group to group for many years. Our earliest Christian writings are Paul's undisputed letters which were written mostly in the 50s C.E. Yet these writings tell us little about Jesus' life. Only with the writing of what we know as the Gospel of Mark do we have our first surviving writing of a narrative of the life of Jesus. Most scholars will date Mark to the late 60s or early 70s C.E. As noted before, the gospel attributed to Mark is formally anonymous. There is no place in the text of the gospel where the author provides a self-identification. Presumably the first audience of the gospel knew who the author was and accepted his authority.
Skip several years into the future and our second gospel was written, the gospel attributed to Matthew, usually dated to the mid to late 70s C.E. There is strong evidence that the gospel known as Matthew was copied in large part from the gospel attributed to Mark. This gospel too is also formally anonymous with no author identification within the gospel itself. Once again, the authority of the author was probably known by the original audience of the gospel.
Yet a few more years later comes a third gospel, that attributed to Luke and usually dated in the late 70s to the 80s CE. Once again, Luke's gospel copied large portions of Mark, and also either copied other portions of Matthew, or Matthew and Luke had a common source that has not survived (called Q, or Quelle for "source"). Interestingly, there is some author self-identification in Luke, though no name is given. In the gospel preface, the author claims to know of other accounts (gospels?), to have relied on eyewitnesses (though he himself is not one), and to have carefully investigated the matter. Though this gospel does not claim to be written by a disciple, it is claiming authority based upon the author's careful research. This might be seen as the first step toward needing to argue for the authority of a gospel, presumably because the amount of time that has transpired between the events described and the time of the writing.
Finally, the fourth gospel, that attributed to John, is written, probably in the 90s CE, and stands apart from the other three in its style and narrative. John also has some self identification of the author in chapter 21, where the authors are a "we" who are dependent upon the testimony of one of Jesus' disciples, the "beloved disciple." Interestingly, the "beloved disciple" from this gospel is never identified by name. Here again, we see a further step in claiming authority for a gospel, this time tracing the contents to the gospel to a disciple, but an unnamed one at that.
As we get into the second century, a couple of things happen. First, new gospels are written, but these mostly come with claims of apostolic authorship like the Gospel of Thomas or the Protoevangelium of James (see post here). In these gospels, the author self identifies as one of the apostles. Yet, their second century date clearly precludes the possibility of apostolic authorship. You could say that as time passes and we get into the second century, 100 years or more after Jesus' death, the claims for authority need to be stronger and stronger. Coincidentally (or perhaps not) it is at this time that we have our first mention of gospels written by Matthew, Mark, Luke, and John. Many scholars conclude at this point that, amidst competition among gospels for authority, it was necessary to attach authoritative names to the four gospels that would later be included in the canon. Thus, the titles Matthew, Mark, Luke, and John, were attempts by Christians in the second century to preserve the authority of those four gospels but do not represent the original authors. This then explains scholars claims that 1) the gospel titles were added later than the composition of the gospels, and 2) the four canonical gospels are anonymous.
These four gospel titles were settled sometime in the second century, and by the third century our manuscripts demonstrate a consistent naming of the four canonical gospels as Matthew, Mark, Luke, and John.
Now, there is one serious objection to the above reasoning, and I think it is a valid one. If second century Christians needed to attach authoritative names to the four anonymous gospels that would later be canonized, why did they choose the names they did? Now, this objection does not confront the gospels of Matthew and John, since those men were disciples and eyewitnesses. Yet, why choose Mark and Luke? Neither of them were disciples nor eyewitnesses. The best connection that can be made is that Mark was connected with Peter and Luke was connected with Paul. Yet, if one were free to choose names, wouldn't one of the disciples be a better option? For this reason, I think that there may be some validity to the traditions of the titles Mark and Luke, that is, that these gospels may have indeed been composed by men named "Mark" and "Luke.". Yet, even saying that, there is no firm evidence that Mark = John Mark of Acts, or that Luke = Luke the Physician from Paul's letters. Those identifications appear to me to be attempts to connect the common names Mark and Luke with anyone in the New Testament by those names who might preserve some "apostolic authority" for these gospels.
Here ends my discussion of gospel authorship for now. We can continue in the comments section.