The term "Mormon" was coined as a pejorative term early in the church's history due to our church's acceptance of extra-biblical scripture (The Book of Mormon). In the writings of earlier LDS (Mormon) leaders, when referring to themselves by the term "Mormon," it was frequently written in quotes " " to indicate that the term was being applied to them by others, and that it was not how they wished to be called. Over time the term shifted to one that was tolerated by the church, and eventually became something to be proud of. I remember Pres. Benson (a past LDS prophet) quoting (he may have been singing it, I don't remember) a song that went "I might be envied by a king, for I am a Mormon boy." In fact, I remember singing that song a few times in my primary days. Today, the church still prefers its official name above all others, but we members are often heard referring to ourselves as "Mormons." As for me, I prefer "Latter-day Saints" or "LDS."I always found it funny (not in a haha way either), that "Christian" Churches, like the Baptist, Methodist (which I have to tread carefully, my gf is Methodist), Episcopalian etc etc, are just that "Christian" churches, yet, here we have the Church of JESUS CHRIST of Latter Day Saints, and they're known as MORMONS, not CHRISTIANS....ummm...huh...weird.
I'm not a MORMON, just something I have noticed...
Another contributing element to our not being commonly called "Christian" like other Christian faiths, such as the ones you named (Methodists, Baptists, etc.) is that our extra-biblical scriptures, and some of our core beliefs (such as the nature of the Godhead/Trinity) and practices (vicarious ordinances for the dead) are offensive to many Christians, and we are not actually considered Christians by much of Christianity. Add to that the fact that we evangelize other Christians (the "why" is another discussion altogether), and we are frowned upon by a great many. Even in this forum, discussion of our unique doctrines can only occur in the Unorthodox Theology sub-forum, which is a nasty place most of the time, by the way. (there are a bunch of folks who have been camping there for years, some of them ex-Mormons, who feel the need to "protect the world" from our duplicitous and shifty presentation of LDS theology—they claim that we don't tell "the whole truth," so that we can ensnare people. Of course, we LDS feel that they don't tell the story right, so mortars often get lobbed. )
Anyway, there's the skinny on why we're called "Mormon" instead of "Christian."