3. Why would his name not be prefixed to the Epistle? In what sense he might say, Hebrews 2:3, that salvation was confirmed to Him by hearers?
Now, Saint Paul did not prefix his name to the Epistle, according the custom generally used in his remaining Epistles, either for modesty’s sake, because κυρίως, by settled agreement, he was the Apostle of the Gentiles, not of the circumcision or Jews, Galatians 2:9, and so he was unwilling to be seen to do anything else, περιεργάζεσθαι, to be a busybody: or because he would not provoke the Hebrew by setting his name, hated by the Hebrews, down first; especially since among them he labored under suspicion, as if he were despising the law of Moses, and urging defection from it, Acts 21:21. Neither is it really a hindrance that the author of this Epistle in Hebrew 2:3 professes that the salvation, which began to be preached by the Lord, was confirmed unto him by the hearers, by which words he appeared to some to make himself a disciple of the Apostles, which Paul was not. For those words, εἰς ἡμᾶς, unto us, that is, that salvation was confirmed by those that heard, are easily understood by customary ἀνακοίωσιν/sharing or communication, which sort is found in 1 Corinthians 10:8, 9; Hebrews 6:1; 10:26; 12:12; 1 Peter 4:3. Moreover, Paul, having been ἀμέσως/immediately called by Christ indeed, was nevertheless βεβαιωθεὶς/confirmed[1] by Ananias, Acts 9:17, 18, and by others, Romans 1:12, and much more by those that had seen Christ, 1 John 1:1, at least through their miracles. But those words, εἰς ἡμᾶς, unto us, are also able to mean, all the way to us or to our times. Finally, it is not the case that the mention of Catechetical doctrine in Hebrews 6:1 does not agree with the era of Paul, since he also made mention of milk, 1 Corinthians 3:1, 2, wherewith he nourished children in Christ; and in Acts 18:25 mention is made of Apollos, κατηχημένου τὴν ὁδὸν τοῦ Κυρίου, catechized in the way of the Lord. Whoever desires to know more about the author of this Epistle, he may consult the most learned diatribes of the Most Illustrious Spanheim on this topic.
[1] Hebrews 2:3: “How shall we escape, if we neglect so great salvation; which at the first began to be spoken by the Lord, and was confirmed (ἐβεβαιώθη) unto us by them that heard him…”
Dr. Dilday's Lecture: "A Pauline Miscellany, Part 4"