The Savior provides his own commentary on why the church among the Nephites should be called after his name. This interaction reminds us why “Mormon” is not the preferred name for our church, For if a church be called in [Mormon’s] name then it be [Mormon’s] church. Most likely, others would not wonder whether or not we are a Christian church if they knew us by our real name. Hence, as far as names go, “Mormon Church” is no better than “LDS Church,” “Church of Moses,” “Church of Abraham,” “Church of Luther,” or “Church of Calvin.”
However, “The Church of Jesus Christ of Latter-day Saints” was not always the official name of the church. For the first 8 years, the church was known by other names, including: “The Church of Christ,” “The Church of Jesus Christ,” and “The Church of the Latter-day Saints.” The revelation giving the full name came in 1838, in Far West (see DC 115:4). The specification, “of Latter-day Saints,” is added to distinguish the church from previous dispensations.
Milton R. Hunter
“The early Christians in the Mediterranean world took upon themselves the name of Christ. As you all recall, they were known generally as Christians. But as their numbers began to spread and become rather numerous in the Mediterranean world, and as the seeds of apostasy began to grow, about 185 A.D. the leaders decided to change the name to Catholic, meaning universal. Thus by choosing to call themselves ‘Universal’ they lost the name, or set aside the name, that God had decreed would be the only name given under heaven whereby mankind may be saved.” (Conference Report, Oct. 1952, p. 38)
LeGrand Richards
“The matter of the name his Church should bear was of great importance to the Savior…Thus the name of the Church was not obtained through study or research, but by revelation direct from the Lord. Does it not seem incredible that of all the churches in the world, there was not one that bore his name when the Lord restored his Church in this dispensation?” (A Marvelous Work and a Wonder, pp. 135-6 as taken from Latter-day Commentary on the Book of Mormon compiled by K. Douglas Bassett, p. 459)