The place “called MORMON, . . received its name from the king” (Mosiah 18:4), but it does not say which king it was named by. Perhaps King Zeniff or his son King Noah named it. We are not told. The later personal name Mormon is derived from that geographical name: “I am called MORMON, being called after the land of MORMON” (3 Nephi 5:12).
The likeliest etymology of the name may be sought in the ancient Egyptian proper name Mry-‘Imn, “Beloved of ‘Amon” — using the name of the Egyptian god ʼAmun,[1] the god of Thebes, and supreme god of Egypt,[2] whose name is known to have been borrowed by several Semitic languages as ʾĀmôn.[3] After all, one Jewish king was named Amon (II Kings 21:18), and there was a king of the Ammonites, who wears an Egyptian crown.[4] Moreover, is this Egyptian etymology one of the reasons why King Lamoni mistakenly believes Ammon to be the “Great Spirit”? (Alma 18:2-5, 11, 16-36, 19:25-27).
Matt Bowen demonstrates how this etymological base is used for several puns (Mosiah 18:8-11 ,21,28,30, Alma 5:3-6,26, Mormon 3:12, Moroni 7:47-48, 8:16-17), and he applies the same understanding of the etymology to the name MARY.[5]
[1] H. Nibley, Lehi in the Desert, etc., Collected Works of Hugh Nibley V (Provo: FARMS/ SLC: Deseret, 1988), 21, 23, 25, 29-31.
[2] Brown, Driver, Briggs, Hebrew English Lexicon, 51, The Enhanced Brown .
[3] Y. Muchiki, Egyptian Proper Names and Loanwords in NW Semitic, 15,43,66.
[4] (List of rulers of Ammon - Wikipedia) (with photo).
[5] Matthew Bowen, “’Most Desirable of All Things’: Onomastic Play on Mary and Mormon in the Book of Mormon,” Interpreter, 13 (2015):27-61, online at http://www.mormoninterpreter.com/most-desirable-above-all-things-onomastic-play-on-mary-and-mormon-in-the-book-of-mormon/