I spoke with some LDS youngsters who came to my door some time back. They're friendly. I learned that they do not like being referred to as "Mormon" but instead prefer "LDS". For them, being called Mormon is derogatory.
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But the new/current prophet hates it and said that God told him he doesn't like the name anymore and that being called Mormon is "a victory for Satin" (the devil).
God is a little inconsistent within Mormonism. First he wanted Polygamy and it was sooo important that he even sent an Angel with a flaming sword down to earth to get them to practice polygamy (even though the prophet was already practicing it in secret at the time). Then in 1904 when the Supreme Court forced the church to stop practicing polygamy or else they would take all assets away. Then magically within days, God told the prophet that its actually ok if they don't do polygamy anymore. Then he hated black people for a while and wouldn't let them into the temple or get the priesthood (which essentially kept them out of heaven according to Doctrine), then changed his mind in 1978 when public pressure was mounting. He didn't want children of Gay people to be baptized in his church for a few years, and then changed his mind after the PR got really bad. Mormon God is heavily influenced by American PR.
The next prophet will probably embrace the name "Mormon" again. So don't stress too much about it. Most active Mormons can't keep track of what doctrine currently is or isn't which is why so many times you get different answers from different mormons about policies and doctrine. Because it really depends which prophets you grew up under, because things change dramatically as they take the helms of power and claim to speak for God.