The nickname "Mormon" was applied early in the history of the Church of Jesus Christ of Latter-day Saints because of church members' belief in The Book of Mormon. This book of scripture tells the story of a group of people who lived on the American continent centuries ago and knew about Jesus Christ because he sent prophets among them. Eventually, a prophet named Mormon compiled and abridged the writings of these prophets. Because Mormon was the principal author, the book was named after him (much like books in the Bible were often named after their authors, i.e., "The Gospel According to Luke").
So the nickname "Mormon" came from a book, which was named after a man who wrote and compiled it under the inspiration of God. Although this is where we often stop when answering this question, we can go further by explaining where this man named Mormon got his name. This is what Mormon himself wrote about his name:
I am called Mormon, being called after the land of Mormon, the land in which Alma did establish the church among the people. (3 Nephi 5:12)Here we learn that Mormon was named after a place called Mormon. What was so important about that place? Earlier in the Book of Mormon, there was a group of people who had forsaken the ways of God. A man named Alma repented of his sins and was called to teach repentance and faith in Jesus Christ. One day as he taught a small group of people who believed his words by a pool of water in a land called Mormon, he pointed to the water and suggested baptism in these words:
As ye are desirous to come into the fold of God, and to be called his people, and are willing to bear one another’s burdens, that they may be light;These verses beautifully describe the covenant we make as we come to Jesus Christ and are baptized into his church. It is a promise to follow God's commandments, stand up for what is right, and relieve the suffering of others. These people did receive baptism, and the Spirit of God was poured out upon them. Later, the book says this about the land of Mormon, where this baptismal scene took place:
Yea, and are willing to mourn with those that mourn; yea, and comfort those that stand in need of comfort, and to stand as witnesses of God at all times and in all things, and in all places that ye may be in, even until death, that ye may be redeemed of God, and be numbered with those of the first resurrection, that ye may have eternal life—
Now I say unto you, if this be the desire of your hearts, what have you against being baptized in the name of the Lord, as a witness before him that ye have entered into a covenant with him, that ye will serve him and keep his commandments, that he may pour out his Spirit more abundantly upon you? (Mosiah 18:8-10)
The place of Mormon, the waters of Mormon, the forest of Mormon, how beautiful are they to the eyes of them who there came to the knowledge of their Redeemer; yea, and how blessed are they, for they shall sing to his praise forever. (Mosiah 18:30)So now we know that the nickname came from a book named after a man named after a place that represents the blessings of redemption by Jesus Christ and the transformation of ordinary people into his disciples who will sing his praise forever.
The message of Jesus Christ is central to the Book of Mormon, and members of the Church of Jesus Christ of Latter-day Saints strive to make Christ, his saving power, and his teachings the center of their lives. We all strive to live up not only to the baptismal covenant described by Alma, but this other statement that Mormon gave about his identity:
Behold, I am a disciple of Jesus Christ, the Son of God. I have been called of him to declare his word among his people, that they might have everlasting life. (3 Nephi 5:13)This is an identity to which every member of our church aspires. We strive to be Christ's disciples. We strive to share his gospel with others so that they can have greater happiness. Because this is the symbol of the place named Mormon and the identity of the man named Mormon, I and millions of others are proud to say: I'm a Mormon.