Question: How many people, named in the Book of Mormon, saw the Savior?
Answer: Twenty-two men are referred to by name in the Book of Mormon as having seen the Son of God.
Three were Jaredites:
the brother of Jared (Ether 3:15)
King Emer (Ether 9:22)
Ether (Ether 13:4)
The other nineteen were descendants of Lehi:
Lehi (1 Nephi 1:8-9)
Nephi (1 Nephi 11:1)
Jacob (2 Nephi 2:4)
King Lamoni (Alma 19:13)
Alma (Alma 36:22)
Mormon (Mormon 1:15)
Moroni (Ether 12:39)
The Nephite disciples: Nephi (brother to Timothy), Timothy, Jonas, Mathoni,
Mathonihah, Kumen, Kumenonhi, Jeremiah, Shemnon, Jonas, Zedekiah,
and Isaiah (3 Nephi 19:4)
“A great multitude” saw the Lord in the land of Bountiful (3 Nephi 11), as did “many” Jaredites (Ether 12:19), but no more names are given.
Source: 400 Questions and Answers About the Book of Mormon by Susan Easton Black, p 39-40.