The following is from chapter 3 in Answering Mormons’ Questions (Kregel, 2013). To get additional help in answering LDS questions, we recommend purchasing the book. Click here to see more.
Generally, Mormons believe their church should be considered Christian. After all, they like to point out how the name of Jesus is in their church’s name. In 1991, Brigham Young University professor Stephen E. Robinson summed up this idea when he asserted, “Is not the name of our church The Church of Jesus Christ of Latter-day Saints? Do we not worship Christ? . . . The Utah Saints shook their heads and wondered how it was possible that anyone could seriously doubt that the Latter-day Saints were Christians.”
Third Nephi 27:8 from the Book of Mormon reads, “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.”
Apostle Bruce R. McConkie referenced this verse when he wrote,
The resurrected Christ gave to the Nephites this test whereby they might distinguish the true church from any other: 1. It would be called in his name, for ‘how be it my church save it be called in my name?’”
It seems odd that such a point even needs to be made. While this certainly could be a concern among some living in Joseph Smith’s time, it is highly doubtful this would have been an issue with people who lived in A.D. 34 or 35, when 3 Nephi 27 was allegedly written. If having the name of Jesus was a requirement to be a “true church,” why didn’t the apostle Paul follow this pattern when he addressed various New Testament churches?
For example, he referred to the Thessalonians in both of his letters as “the church of the Thessalonians.” In Galatians 1:2 he wrote to the “churches of Galatia,” and in 1 Corinthians 1:2 he called the body of believers in Corinth “the church of God which is at Corinth.” These were New Testament churches, but should we assume these congregations were not part of Christ’s true church because Jesus’ name was absent?
Many unfamiliar with LDS history may be unaware that since its founding on April 6, 1830 the church’s official title has not always included Christ’s name. Doctrine and Covenants 20:1 reports that the original name of the church was the “Church of Christ.” In 1834, the name was changed to “The Church of the Latter-day Saints.” 
This took place at a priesthood conference at which Joseph Smith was present. The vote was unanimous. Note that any reference to Christ was completely omitted. This remained the church’s official title until April 26, 1838, when Smith claimed that he had a revelation and was told to change it to the name the church bears today. This meant the church did not have the name “Jesus” or “Christ” in it from 1834 to 1838. Does this mean the LDS Church was not Christ’s church during that four-year span?
Richard Lloyd Anderson, emeritus professor of church history and doctrine at Brigham Young University, attempted to explain the 1834 change. “This alteration was not seen as a deemphasis of Christ,” he wrote. “On the contrary, it was done in hopes that the name of the Church would more clearly reflect the fact that Christ was at its head.”
Anderson believes that even though the official title of the church omitted the name of Christ, it was still known in the minds of many as the Church of Christ, and so he argues that the church’s name really never changed. The name “Church of Latter-day Saints,” Anderson adds, is “descriptive of divine restoration,” indicating “Jesus is at its head.”
Book of Mormon witness David Whitmer did not agree with the 1834 name change. He wrote,
In June, 1829, the Lord gave us the name by which we must call the church, being the same as He gave the Nephites. We obeyed His commandment, and called it the Church of Christ until 1834, when, through the influence of Sidney Rigdon, the name of the church was changed to “The Church of the Latter Day Saints,” dropping out the name of Christ entirely, that name which we were strictly commanded to call the church by, and which Christ by His own lips makes so plain.
Whitmer certainly saw an inconsistency between what the Book of Mormon commanded and how church leaders voted. In addition to the church’s name, Latter-day Saints also point to their church’s doctrinal and structural unity as proof of its authenticity. However, much of this unity can be attributed to the fact that the LDS Church tends to discipline those who express public opposition to what comes forth from Salt Lake City.
Those who openly disagree with church doctrine and policy can be threatened with being disfellowshipped or even excommunicated. Consider also the many “restoration churches” teaching that Joseph Smith was a true prophet of God and the Book of Mormon is ancient scripture. The LDS leadership rejects their claims of authenticity.
Technically, God’s church is not an organization or a building. Rather, the body of Christ is composed of redeemed humans whose sins have been forgiven. In the New Testament, the word church (Greek: ecclesia) appears 115 times. In the great majority of these passages, it refers to a local congregation of believers, but it can also speak of believers everywhere.
Jesus used the illustration of a shepherd (Himself) over a flock (believers), and many other images are used in the New Testament to describe the church, including the bride of Christ, the salt of the earth, and branches of the vine.
Neither the title of a church nor a label a person may be given defines true Christianity. Rather, as John 1:12 says, “But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name.” Christians are saved individuals who by faith in the work of Jesus Christ on the cross at Calvary have been forgiven their sins. God recognizes His people by their trust in Him, not by a name imprinted on a badge or on a sign posted at the entrance of a building where people meet on Sunday mornings.
 Are Mormons’ Christians, p. vii.
 Mormon Doctrine, p. 139.
 History of the Church 2:63.
 A Sure Foundation, p. 195.
 Ibid., p. 196.
 An Address to All Believers in Christ, p. 73.
 For example, President Joseph Fielding Smith referred to the Reorganized Church of Jesus Christ of Latter Day Saints (RLDS), based in Independence, Missouri, as a “spurious organization” (Doctrines of Salvation, 1:261), and Smith’s son-in-law Bruce R. McConkie called the RLDS a “cult” and an “apostate faction” (Mormon Doctrine, 629). The Reorganized Church of Jesus Christ of Latter Day Saints is now known as the Community of Christ.
 See Romans 12:5 and 1 Cor. 12:12, 27.