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But then "LDS" is now out of date as well! The leadership has decided that they don't want to be called "LDS" anymore. They even dumped the wonderfully succinct "lds.org" domain for "churchofjesuschrist.org."
Now they want you to use the full name of the Church (at least the first time referenced in the convo), which is "The Church of Jesus Christ of Latter-day Saints." So for example, if you want to refer to a person you would have previously called "Mormon" or "LDS," you should instead use "member of The Church of Jesus Christ of Latter-day Saints." There is a minor relief though. On subsequent references you can shorten it to "Church of Jesus Christ" or "the restored Church of Jesus Christ."[1]
Personally I like the (still silly long) acronym COJCOLDS. But realistically very few Mormons are going to offended if you call them "LDS."
So there are a handful of factors/motivation at play, but yes a huge goal is to brand themselves more as Christian.