Q. Is it a prohibition to omit the name of the author? Or is it only a mitzvah to mention him?

A. There are prohibitions involved, some of the ones mentioned in Poiskim are:

Midrash Tanchuma (Bamidvar) quotes in the name of Rabbi Yochanan the prohibition of “do not steal from the poor” (Mishle 22:22) as referring to the one who omits the name of the author. See Mogen Avrohom (O.C. 156:2) and Hagaos Rabbi Akiva Eiger (ibid.). According to the Sh’loh (p.53) and others, the above is part of Talmud Nedarim, even though our version of the Talmud does not include it.

Shach (Y.D. 242:43) mentions that he is like “wrapping himself with a mantle that is not his”

Minchas Ytzchak (3:268) quotes a Sifri (Shoftim) that would subject plagiarism to the biblical prohibition of “Lo Sasig” or “You shall not pull back your neighbor’s landmark” (Devarim 19:14).

In taking credit for someone else’s ideas and words, one transgresses on the biblical prohibition of “Distance yourself from a false matter” (Shemos 23:1)

Rabbi A. Bartfeld