I am not a Mormon, but have had many friends that were, and have read the Book of Mormon (I have tried for years to get a copy of the Prophets, but it is nearly impossible unless you have been on a mission even though it is the highest level of authority for them). They would prefer you to call it the 'Church of Christ of the Latter Day Saints' (LDS for short). According to their teachings, Moroni was the name of the angel that brought the Book of Mormon to Joseph Smith. The name 'Mormon', is derived from Moroni, and was used to make fun of the Latter Day Saint's for following Moroni. This is just as the term 'Christian' (literally 'Christ ones') was initially used as a derogatory name for those that followed Christ, or Baptist was originally intended as derogatory for that denomination (which I belong to).

It's the Book of Mormon, the Church of Jesus Christ of Latter Day Saints, and the members are Latter Day Saints.

The term “Mormon,” as has been mentioned, was derived from the Book of Mormon—a book that Latter-day Saints consider to be scripture (along with the Bible and a few other volumes). It was originally a term of derision, having been invented by people that couldn’t get together a big enough mob to go rape, pillage, and murder the “Saints” or the “Christians,” but didn’t have that problem if they came up with a slur, i.e. “the Mormons.” As such, the term (when referring to members of the Church and not the Church itself) is not *technically* incorrect, but it is somewhat frowned upon and some members of the Church do consider it offensive. As for the name “the Mormon Church,” this is never correct, as the Church states in its Media Style Guide. The correct name of the Church is The Church of Jesus Christ of Latter-day Saints. If a shorter version is desired, it is appropriate to use “the Church of Jesus Christ” or simply “the Church” (see http://tinyurl.com/2e7pv4). Regarding where the Church got its name—by which I suppose you mean its actual name, The Church of Jesus Christ of Latter-day Saints—the Lord Himself specified the name in an 1838 revelation, now recorded in Doctrine & Covenants 115 (available online at http://scriptures.lds.org/en/dc/115/4). Hope that helps!

Otter's answer is quite good. I would only add that the original name of the LDS Church was "The Church of Christ". This was to follow a belief in the 19th Century Restorationist movement that a truly restored Church should have Jesus, Christ, or both in the name. In the second iteration Joseph Smith managed to get BOTH in - much to the delight of sign makers who charged by the letter, I'm sure! That's the short version. The LONG version is FAR more interesting! From WikiPedia: "HISTORICAL BACKGROUND In the early 1800s, Alexander Campbell and others began to popularize the idea among Christians in the United States that the division among Christian sects had been caused by a Great Apostasy from the original teachings of Jesus, practiced by the primitive Christian church. Campbell and his associates founded the Restoration Movement, arguing that the true practices of Christianity could be achieved by restoring practices described in the New Testament. The Restorationists also intended to eliminate sectarianism, arguing that there should be only one Christian church and that it should be named, the "Church of Christ." Some historians of religion categorize the Latter Day Saint movement as part of or an off-shoot of the larger Restoration movement, but there are significant differences. While early Latter Day Saints believed in the need to "restore" the "true church of Jesus Christ", they also believed that direct authority from God was essential for the restoration to be valid. Joseph Smith, Jr., the Latter Day Saint movement's founder, claimed to possess that authority as a Prophet who received revelations. Smith's revelations authorized and commanded the organization of the Church of Christ in 1830, and in many of the revelations Smith claimed to receive, God referred to the church by that name. Smith taught that this church was a restoration of the primitive Christian church established by Jesus in the first century A.D. Moreover, Smith taught that this restoration occurred in the "Latter Days" of the world, i.e., the time immediately prior to the Second Coming of Jesus. EARLY CHANGES The fact that the churches of other Christian Restorationists, including the Campbellites, were also named the "Church of Christ" caused a considerable degree of confusion in the first years of the Latter Day Saint movement. Because of the distinct belief in the Book of Mormon among Smith's followers, people outside the church began to refer them as "Mormonites" or "Mormons." Smith and other church elders considered the name "Mormon" derogatory.[2] In May 1834, the church adopted a resolution that the church would be known thereafter as The Church of the Latter Day Saints.[3] At various times the church was also referred to as The Church of Jesus Christ and The Church of God.[4] In the late 1830s, Smith and those loyal to him founded a new headquarters in Far West, Missouri. At Far West in 1838, Smith announced a revelation renaming the organization the Church of Jesus Christ of Latter Day Saints.[5][6] NOTES [2] Carmack, John K. (1989), "Fayette: The Place the Church was Organized", Ensign 19 (2): 15–19, <http://library.lds.org/nxt/gateway.dll/Magazines/Ensign/1989.htm/ensign%20february%201989.htm/fayette%20the%20place%20the%20church%20was%20organized.htm?f=templates$fn=document-frame.htm$3.0$q=$x=$nc=9347>. [3] Jessee, Dean (1976), "Joseph Knight's Recollection of Early Mormon History", BYU Studies 17 (1): 35, <https://byustudies.byu.edu/shop/PDFSRC/17.1Jessee.pdf>. [4] Marquardt, H. Michael (1992), "An Appraisal of Manchester as Location for the Organization of the Church", Sunstone 87 (2): 49–57, <http://www.sunstoneonline.com/magazine/searchable/Issue87.asp>. [5] Smith, Lucy Mack (1853), written at Liverpool, Biographical Sketches of Joseph Smith the Prophet, and His Progenitors for Many Generations, S.W. Richards, <http://relarchive.byu.edu/19th/descriptions/biographical.html>. [6] Smith, William (1883), written at Lamoni, Iowa, William Smith on Mormonism: A True Account of the Origin of the Book of Mormon, RLDS Church, (ISBN not assigned), <http://www.olivercowdery.com/smithhome/1883Wilm.htm>." Attached Images: 1) Interior Shot of an 1830 Book of Mormon 2) Today's Official Logo imposed over the statue of Christ that greets visitors in the Temple Square Visitor's Center, Salt Lake City

It's my understanding from talking with a member, that they are called Latter Day Saints after the Saints of the last days as written about in DANIEL, where it says "All their lawless deeds will be forgiven and they will rule the world forever" Amazing that they believed this allowed them to kill nearly everyone on the Fancher wagon train (and steal all their eartly goods) so they could use them to "bring in the Kingdom." Didn't Christ say that in the END many would say "LORD, LORD. Didn't we do all these things in your Name." Remember HIS answer?