Heidegger's Bible Handbook: Matthew: Title
2. Why is the Gospel called κατὰ Ματθαῖον, according to Matthew?
This Gospel is called κατὰ Ματθαῖον, according to Matthew, that is, written according to the narration committed to writing by Matthew. For it is not without good reason written, κατὰ Ματθαῖον, according to Matthew, rather than Ματθαίου, of Matthew. For the old inscription was: Εὐαγγέλιον Ἰησοῦ Χριστοῦ, the Gospel of Jesus Christ, as it is in Mark 1:1: for the argument of the book was the Gospel preached by Christ, and concerning Christ. Therefore, the name of the writer was not able to be set down. Just as we do not say: Vita Cæsaris Plutarchi, The Life of Cæsar of Plutarch:but rather written by Plutarch. Hence, the Gospel according to Matthew is nothing other than the doctrine delivered by Christ and concerning Christ, as it was committed to writing by Matthew.
Mestrius Plutarchus (c. 46-127) was a Greek historian.