The Book of Mormon was written for our day, but ever since the days of Nephi, it was known that the organizational structure of God’s kingdom should be named after Christ. He refers to the Church of the latter-days as the Church of the Lamb of God (1 Nephi 14:10,12). Later, the Savior explains why the name of the church is so important:
’…therefore ye shall call the church in my name…
And how be it my church save it be called in my name? For if a church be called in Moses‘ name then it be Moses’ church; or if it be called in the name of a man then it be the church of a man; but if it be called in my name then it is my church, if it so be that they are built upon my gospel.’ (3 Nephi 27:7-8)
The Church of Jesus Christ of Latter-day Saints was organized on April 6, 1830. However, the full name was not used until it was given in a revelation in April of 1838, thus shall my church be called in the last days, even The Church of Jesus Christ of Latter-day Saints (DC 115:4). Prior to that time, one of the names of the early church was the Church of Christ (DC 20:1) just as it was called by Alma and his people.
George Albert Smith
“I would like to suggest to you, my brothers and sisters, that we honor the name of the Church. It is not the church of James and John, it is not the church of Moroni, nor is it the church of Mormon. It is the Church of Jesus Christ. And while all these men were wonderful and notable characters, we have been directed to worship God in a church that bears the name of his Beloved Son. I wish that our young people as they grow up would keep that fact in mind. We have become so accustomed to being called the Mormon Church by all our friends and neighbors throughout the world, that many people do not know the proper name of the Church, and I think the Lord would expect us to let them know that.” (Conference Reports, Oct. 1945, p. 168)