The term Mormon was used as a pejorative name to the believers in the Book of Mormon from which the word has it’s origin. So Mormon is a Book of Mormon believer.
Mormon or Mormonite was first used in 1830, however the Church started in 1970 using to refer itself as such.
About the origin of the word, according to Joseph Smith it came from the “Egyptian, “mon.” Hence, with the addition of “more,” or the contraction, “mor,” we have the word “mormon”; which means, literally, “more good.”
At the other hand the President Gordon B. Hinckley in a speech in 1990 denied such statement when said that he “knew, of course, that “more good” was not a derivative of the word Mormon. I had studied both Latin and Greek, and I knew that English is derived in some measure from those two languages and that the words more good are not a cognate of the word Mormon.”
However he adopted the prophet statement that Mormon should mean “more good”
He also recognized that “regardless of our efforts, we may never convert the world to general use of the full and correct name of the Church. Because of the shortness of the word Mormon and the ease with which it is spoken and written, they will continue to call us the Mormons, the Mormon church, and so forth.”
“We may not be able to change the nickname, but we can make it shine with added luster” and that is exactly what the Church started to do, adopting using and monopolize the nickname Mormon.
So, something that we must remember that the nickname does not belong to the Church and because the origin of the name is to those that follow Smith teachings and accept the Book of Mormon as scripture, then the term should be borrow also to all the sects of the Mormonism. If the main Church derivate in many schismatic churches and still kept the main origin then they are Mormons. Hence LDS Mormon, Reformed Mormon, Mormon fundamentalist, etc.
Recently the Public Relations department publish style guides to refer to the church, where we see that ” While the term “Mormon Church” has long been publicly applied to the Church as a nickname, it is not an authorized title, and the Church discourages its use.” Furthermore try to deny it use “when referring to people or organizations that practice polygamy, the terms “Mormons,” “Mormon fundamentalist,” “Mormon dissidents,” etc. are incorrect. The Associated Press Stylebook notes: “The term Mormon is not properly applied to the other … churches that resulted from the split after [Joseph] Smith’s death.”” But who gives to the Church such power? Since the term is not native from a member of the Church but from non-members, the Church should encourage the proper name of the Church instead of steal a well known term, worse, trying to limit it use.
But the Church goes further, in some countries, Mormon and some phrases including the term are registered trademarks owned by Intellectual Reserve, Inc. In the United States, the LDS Church has applied for a trademark on “Mormon” as applied to religious services; however, the United States Patent and Trademark Office rejected the application, stating that the term “Mormon” was too generic, and is popularly understood as referring to a particular kind of church, like “Presbyterian” or “Methodist”, rather than a service mark. The application is on appeal as of mid-200.
The only reason I can find is that the Church could be linked to practices that she doesn’t believe anymore, but the Church should realize that have sisters churches like it or not. The Church struggle so hard to be accepted with the nickname Christians (monopolized for another group) but then don’t realize that they are been treated the same way it treats other Mormon Churches: You can’t hold that nickname because you don’t practice our practices, our believes and doctrines.