I recommend an article by Armin D. Baum (also one of the few present scholars working on Papias) entitled “Anonymity in the New Testament History Books. A Stylistic Device in the Context of Greco-Roman and Ancient Near Eastern Literature” NT 50 (2008): 120-142. He begins with the problem of the anonymity of the 5 historical NT books (Gospels, Acts) and M. Wolter’s observation that Luke’s prologue (1:1-4) felt that “apostolic tradition” rather than named authorship was enough to guarantee authenticity and authority (121). Here the NT books stand out from Greco-Roman historiography (Luke’s prologue is the closest but this makes absence of authorship even more striking): their superscriptions (“Gospel according to X”) are secondary, they lack an explicit mention of author unlike for instance the Coptic Gospel of Thomas (“Didymus Judas Thomas wrote”) and the first person singular/plural in Luke-Acts and John (Luke 1:1-4; Acts 16:10-17; 20:5-8, 13-15; 21:1-18; 27:1-2; 28:1-16; John 21:24) is ultimately anonymous and may be editorial in John (121-122). Baum gives an overview of 3 prior explanations on pp 123-24: 1) E. Meyer compares the anonymity of the 4th Gospel with Xenophon’s pseudonymous claim that his Anabasis was written bya Themistogenes of Syracuse but Greek and Roman historians almost exclusively published under their own names, 2) A.J.M. Wedderburn argued that anonymity emphasized the evangelist’s complete dependence on tradition rather than firsthand witness but what of seeming witnesses claim in John and Luke-Acts and are there parallels for anonymous handling of tradition, or 3) M. Wolter sees anonymity as a specifically Christian phenonmenon (Jesus is the authoritative spokesman and authorship irrelevant) but then why is Acts anonymous if it doesn’t relate words/deeds of Jesus (and why didn’t Paul write anonymously) and this lean too much towards the NT writings as sui generis.
Baum argues that a prologue in Greek historiography was the norm (cf. Lucian, De hist. conscr. 23) (Xenophon’s Hellenica seems like an exception but he may see it as a sequel to Thucydides work) and included publishing under one’s name and provenance (“Hecataeus of Miletos”; “Herodotus of Halicarnassus”; “Thucydides of Athens”; “Josephus, son of Matthias”; other Jewish historians like Eupolemus [157/158 BCE], Artapanus, Cleodemus Malchus und Theophilus [100 BCE]. Justus of Tiberius [1st cent CE rival of Josephus]; the prologue to Arrian’s Anabasis may be an exception but likely Arrianos in the title, Xenophon’s Anabasis is pseudonymous). The same applied to biographies (Euripides, Isocrates, Lucian, Philo, Plutarch, Suetonius) though the Lives of popular literature (the Vita Aesopi, the Vita Alexandri Magni (later ascribed to Callisthenes], Lucius seu asinus, Vita Secundi philosophi) may be exceptions. Of 42 ancient epitomes, only 7 are anonymous (124-27). According to the conventions of Greco-Roman historiography the one who collected (interviewed/sifted reliable witnesses, compiled rough notes of hypomnemata) and added literary artisty to a historical work ought to sign their name (cf. Lucian, De historia conscribenda), though another motivation to write one’s own name was the desire for fame and the survival of one’s name for posterity (131-34). In contrast, historical narratives in the Hebrew Bible are anonymous and later named after a main character (Joshua, Judges, etc) as are some later Jewish works (Tobit, Judith, Joseph and Aseneth, Maccabeed [though 2 Macc 2:24 credits Jason of Cyrene as a main source). This fits into the rest of ANE historical writing (Acadian, Mesopotamian, Egyptian) and even after the influence of Greek conventions after Alexander the Great many Jewish writings are still anonymous (cf. Qumran). 2 Maccabees adopted the Greek prologue convention but does not name the author, nor does the prologue of the Wisdom of Ben Sira (127-30). Discounting older views that these authors left out their names because they did not want to subtract from divine inspiration (then why aren’t all biblical books anonymous) or because they were intended only for a limited close circle (were texts like the Gospels only intended as private writings?) (134-35), he argues that the HB and NT books follow Ancient Near Eastern Historians in having a narrator who disappears because the subject matter is given absolute priority, in more direct speech of the characters in the narrative and in more closely following ones source texts (136-37). This does contrast with the named prophetic or wisdom books in the HB and ANE, but the reason is that the authority of the wisdom or prophetic material in those cases depends on the authority of the sage or prophet (139). Thus, Mark and Matthew take up the style of the HB historical book, while Luke-Acts moves closer to Greco-Roman conventions but remains anonymous like 2 Maccabees (130). The NT authors follow the HB historical books in giving maximum priority to their subject matter of which they were only insignificant mediators; even Papias regards the evangelist Mark as only a transmitter of Peter’s memories yet his interest in named authors signals a new shift in defending the authenticity and reliability of the Gospels from naming the authors and this comes more and more into focus (he gives the example of the debates of Tertullian and Marcion, the later Gospel titles, Salvian of Marseille trying to justify his own pseudonymous work) (140-42).
Overall, I think this article make a strong case for why our Gospels are anonymous. It makes sense that the Jewish authors of the Gospels (though the author of Luke-Acts might have been a Gentile, though perhaps a former “God-fearer”?) were indepted both to Jewish and Greco-Roman thought-worlds in composing their writings, both influenced to invest the Life of Jesus with scriptural authority and set it in the context of the unfolding story of Israel and also influenced by the Greco-Roman genre of bioi. I think the argument definitely works for Mark, for which I had mentioned that the only thing that matters for the author is “the good news of Jesus Christ.” For John, I wonder if we are beginning to see a move towards explicitly identifying the author or main source of the tradition in the figure of the “Beloved Disciple”, though is the epilogue which includes the claim that the Beloved Disciple is “the one who wrote these things” (Jn 21:24) original to the Gospel or a later addition? Even in the case of Luke-Acts where his prologue seemed designed to connect with a more elite Hellenistic audience, it would be interesting to compare this article with Loveday Alexander’s argument in The Preface to Luke’s Gospel which argues that the Lukan prologue does not conform to ancient historiographical prologues but scientific prefaces (e.g., a teacher passing philosophical instruction or a how-to-manual in a trade to a student). Again, is the enigmatic “we” that sporadically appears an attempt to make a claim about authorship or is this some other literary device to give the reader a feeling of participating in the events being recounted? Why do you think the Gospels are anonymous?