According to Evan, the author of Elm:
I wanted to name it after a tree (nice names, not too much namespace pollution). I made a big list of pleasing tree names and noticed that Elm sounded quite like Element. That's pretty much it :)
14 June 2013 -
original source on archived Google Groups
I wanted a tree name, and elm sounds a bit like Element. No awesome backronyms so far afaik :P
20 Nov 2013 -
@evancz on Twitter