No one knows.
A study of the terminology, themes, and grammar had led scholars to a rather firm conclusion that the author of Hebrews was not Paul.
- Its language and style of origin are not like Paul
- Its OT citations are *always* direct citations of the Septuagint. Paul never did that.
- It's anonymous. Paul signed his letters.
- Heb. 2.3 indicates that the author never had a direct personal revelation from God.
Many other authors have been suggested: Luke, Silas, Philip, Priscilla, Clement of Rome, Apollos, or Barnabas. No one knows. There are precious few clues in the text itself. Generally it is thought to be a second-generation Christian, well-versed in the study of the Septuagint, which he interpreted according to a creative exegetical principle. He had a copious vocabulary and was master of a fine rhetorical style, completely different from Paul’s. He was a Hellenist. That doesn't take us far enough to be able to make any kind of reasonable guess as to a name of the author.