See part I here.
On the last page of the May 1834 issue of Evening and the Morning Star, the Church included the minutes of a meeting held on May 3, 1834. In a straightforward way, and lacking any fanfare, it included the following:
After prayer the Conference proceeded to discuss the subject of names and appellations, when a motion was made by Sidney Rigdon, and seconded by Newel K. Whitney, that this church be known hereafter by the name of THE CHURCH OF THE LATTER DAY SAINTS. Appropriate remarks were delivered by some of the members, after which the motion was put by the moderator, and passed by unanimous voice.
Resolved that this Conference recommend to the Conferences and Churches abroad, that in making out and transmitting Minutes of their proceedings, such minutes and proceedings be made out under the above title.
Unfortunately, they did not include any of the discussion preceding Rigdon’s motion or any of the remarks given afterward. However, there was an editorial included in that same issue which sheds light on the thinking behind the name change (or at least how they expressed it). Entitled “The Saints,” this article by Oliver Cowdery presented a logical explanation on why a name of the Church is important, and in doing so provided a great example of how Mormons used rational thought to prove their supernatural claims.
To begin the article, Cowdery expresses his disgust at the Church being labeled as “Mormon”: “Others may call themselves by their own, or by other names, and have the privilege of wearing them without our changing them or attempting to do so, but we do not accept the [title of Mormon], nor shall we wear it as our name…”—a rhetorical practice we have seen repeated a couple times in recent years. This argument is crucial to Cowdery’s argument, however, because he will then go on to explain why the name a church chooses for itself is so important.
Cowdery then goes on to explore the significance of many religions calling themselves the Church of Christ, or claiming that their church has God’s divine truth. “This thing is certain,” he reasons, “if one is right, all the others are wrong.” Indeed, if there are “those professing a belief in the bible, or and not only professing a belief but to be followers of the doctrine contained in the same,” then it is reasonable that those churches’ beliefs should be compared to those of the bible. This is because God’s truth, church, ordinances, and even worship must be the same throughout all time, or else God would be a changing God:
If it is urged that the ancient Saints were a different people in worship, had different ordinances, were partakers of other joys and privileges, and all this was necessary for their salvation, might we not with propriety ask, why was this necessary for them, and is now unnecessary for those whose profession says they are heirs of the same kingdom, children of the same Parent, and are expecting to be equal sharers with them in those joys which never fade, in that house not made with hands?”
Cowdery then engages the dynamics involved when Christ set up his church in the meridian of times. Those who followed Christ were required to be repent, be baptized, follow correct teachings, and do all else the Savior asked. “In short,” Cowdery reasoned, “they were the church of God, they were his SAINTS.” Unfortunately, this group of saints was then “separated into different parties,” and the doctrines, ordinances, and practices of the Lord were lost. It is no wonder then, according to Cowdery, “that those who have departed from the course which the ancients were required to persue[sic]…should now substitute other names” in the place of what Christ’s church was originally called. Therefore, this is an acknowledgement that “none of [the other churches] pretend that God has ever spoken to them,” since they do not accept the designated title for God’s church.
While this might not be the main reason the Church changed its name in 1834, it is at least how they explained it to others. They used the simple idea of what the name of a Church should be, and used it to signify the validity of their religion and the apostate status of others. More important than even being bearing the name of Christ is bearing the name of the original church Christ set up—the Saints. Thus, by using deductive reasoning—the rationalized approach of determining the significance of a name—they tried to prove the truth of their supernatural claims: that they are the same divinely organized religion that Christ set up when on the Earth.
 “Communicated,” The Evening and the Morning Star 20, May 1834: 160. The Church had up until this point been known as the “Church of Christ.”
 Oliver Cowdery, “The Saints,” The Evening and the Morning Star 20, May 1834: 159, emphasis in original.
 Ibid, 158-159, emphasis in original.
 Ibid, 159, emphasis in original.
 Some historians, most notably Marquardt and Walters, have argued that the name change was related to escaping their debts, though I am not sold on their argument. There always could be, however, some other major reason influencing the name shift that I am just not aware of (and knowing my luck someone will correct me and give an obvious explanation).