Encyclopedia of Mormonism – Name of the Church

‍https://eom.byu.edu/index.php/Name_of_the_Church  

Author: Black, Susan Easton

The name The Church of Jesus Christ of Latter-day Saints was given by the Lord in revelation to Joseph Smith on April 26, 1838 (D&C 115:4). The Church had been known as The Church of Christ from 1830 to 1834 (D&C 20:1); The Church of the Latter Day Saints in 1834; and The Church of Christ of Latter Day Saints from 1836 to 1838. The Church is commonly, but unofficially, referred to today as the Mormon Church and its members as Mormons because of their belief in the Book of Mormon. But the use of the term "Mormon" to refer to the Church is unsatisfactory from the point of view of Church members because it does not convey the conviction that Jesus Christ is the head of the Church and that members strive to live Christian lives. In the Book of Mormon, Christ's disciples asked him, "Tell us the name whereby we shall call this church" (3 Ne. 27:3). He answered, "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 Ne. 27:8). By implication, calling the Church by the name Mormon would make it Mormon's Church. While most Church members are not offended by the title Mormon, they prefer the name that properly underscores their relationship to Christ.

Members of the Church are often referred to as saints, meaning men and women who are committed to live in accordance with the gospel. The New Testament similarly refers to followers of Christ as saints. The term "Latter-day" comes from the belief that the world is passing through the last days prior to the second coming of Christ.

The Correct Name of the Church – President Russell M Nelson

https://www.lds.org/general-conference/2018/10/the-correct-name-of-the-church?lang=eng 

It is the command of the Lord. Joseph Smith did not name the Church restored through him; neither did Mormon. It was the Savior Himself who said, “For thus shall my church be called in the last days, even The Church of Jesus Christ of Latter-day Saints.”

Even earlier, in AD 34, our resurrected Lord gave similar instruction to members of His Church when He visited them in the Americas. At that time He said:

“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.”

Thus, the name of the Church is not negotiable. When the Savior clearly states what the name of His Church should be and even precedes His declaration with, “Thus shall my church be called,” He is serious. And if we allow nicknames to be used or adopt or even sponsor those nicknames ourselves, He is offended.