Why would they want to do that?
There is a negative connotation to the name "Baptist" among a large number of Americans, and it isn't just recently from the Westboro church's reputation (they aren't affiliated with any Baptist denomination anyway). People still believe the Southern Baptist church in town doesn't approve of dancing, drinking, and preaches fire-and-brimstone-hellfire-and-damnation -- in other words, strict legalistic pap (I'd use another term, but, in the words of George H.W. Bush, "it wouldn't be prudent"). Unfortunately, in some cases, those opinions are correct. Small-town churches of every stripe tend to be slow in growth in their doctrine, being influenced by generation upon generation of the same families, which tend to cling to old concepts, right or wrong.
What many people fail to realize -- including many baptists themselves -- is that such attitudes, while still existing in a great deal of small town Baptist churches, Southern or otherwise, it isn't what the Southern Baptist doctrine is today. My wife was somewhat trepidatious in beginning to attend my SBC affiliated church when we first started dating. She had been pretty much shunned and left to deal with life on her own when she filed for divorce from a drunkard husband who, among other things, would pick up their children while they were separated drunk as a skunk and drive them to his parents' home where he was staying. There he would continue to drink, pass out, and leave the kids to play among themselves or be entertained by granddad and grandma, who all along were telling my wife "It's your problem, not ours." This from her father-in-law, the head deacon at the church! That was in a small town SBC church on the northern fringes of Kansas City, Missouri (by the way, for clarification, when someone says "Kansas City" they are almost always talking about KCMO -- KCK is is the armpit (or worse) of Kansas, except for where the speedway is located).
That experience colored her opinion of SBC churches. So naturally she wasn't sure about beginning to attend another one, especially given her Disciples of Christ background. She was amazed at the strength of teaching, the love shown to her as my friend and guest, and was quickly won over. She's going to be joining the church later this month (she's a NICU nurse and works each of the next two Sundays).
Many people have similar experiences with one church and automatically assume all SBC churches are like that. For that matter, many people form that opinion of just about any denomination based on one bad experience with one church. Because the SBC is the largest non-Catholic denomination in the U.S., it is not surprising the SBC has this larger reputation among conservative churches. There are more SBC churches, therefore -- especially given the SBC's penchant for the autonomy of the local church -- there are going to be more instances of local churches being bad examples.
So, having gone on for sometime here (sorry), I will conclude by saying that some Baptist churches change their name to get away from the erroneous misconceptions people have of Baptists and Baptist churches. Also, most people don't know that there are over 200 Baptist denominations in the U.S., aside from the SBC, so that misconception is largely undeserved. The fact is, there are a lot of legalistic Baptists, in all denominations, including the SBC. They aren't living or breathing either the Bible, or their churches doctrine (with exceptions: Some Baptist denominations are just plain legalistic). Tendency toward legalism lends to this reputation so that any church with the name "Baptist" on the door or the sign gets painted with the same broad, erroneous brush.
That's why so many change their name to something that proclaims their faith, without revealing (and I don't think it is dishonest) they are Baptist-affiliated.