First of all, any and all available manuscripts of the four gospels have the same titles designating their respective authors. All copies of Matthew have the same name. All copies of Mark have the same name. All copies of Luke have the same name. All copies of John have the same name. The titles of the traditionally attributed authors are present on all of the manuscript copies of the gospel narratives.
Secondly, we have no early Christian rejection of the traditional authorship of the four gospels. A few examples of patristic support would include Irenaeus, Papias, Tertullian, and the church historian Eusebius. There exists no other tradition which conflicts with conventional claims of authorship.
Thirdly, the four gospels are named after relatively unimpressive individuals. Matthew was a tax collector. Luke was not even an apostle. If the four canonical gospel narratives were forgeries, then it would have been far more probable that the authors used names of better known people such as Peter or Thomas. After all, that is the pattern we observe amongst heretics who produced their spurious works during the second and third centuries.
Fourthly, the liberties provided through the gospel give credence to the traditional authorship of the four gospels. If they were forgeries, then how come the authors did not simply make up an easier path to worship God? Why would the early Christians follow a way of life that would result in them being persecuted? Even the Jews allowed sacrifices to be offered to the Roman Emperor.
How come the four gospel narratives contain embarrassing details regarding the twelve apostles? For instance, Peter denied Jesus Christ three times in a row (Luke 22:54-62). Matthew records Christ calling Peter Satan and a stumbling block (Matthew 16:23). Judas betraying Him to the chief priests and students of the Law also serves as a perfect example of embarrassing details. Paul prior to his conversion persecuted Christians. If the four gospel narratives were forgeries, then we should not expect their authors to incorporate such shameful and humiliating details regarding these people.
Even if it could be proven beyond a reasonable doubt that the original canonical gospels were anonymous, that point by itself would still not rule out traditional authorship attribution. Professor Michael J. Kruger provides these insightful comments:
"For one, this did happen from time to time with Greco-Roman biographies. We do have examples of formally anonymous biographies, so this would not have been unheard of (e.g., Lucian’s Life of Demonax, Secundus the Silent Philosopher, Lives of the Prophets, Arrian’s Anabasis, and Sulpicious Severus’ Life of St. Martin ). But, Armin Baum has suggested another, and even more fundamental reason. Baum has argued that the Gospels were intentionally written as anonymous works in order to reflect the practice of the Old Testament historical books which were themselves anonymous (as opposed to other Old Testament writings, like the prophets, which included the identity of the author). Such a stylistic device allowed the authors of the gospels “to disappear” and to give “highest priority to their subject matter.” Thus, the anonymity of the Gospels, far from diminishing their scriptural authority, actually served to increase it by consciously placing the Gospels “in the tradition of Old Testament historiography.”