I read an article about this a few years ago, and the answer is whatever they want. I remember one couple said they just decided they liked the wife's grandmother's maiden name, so they just picked that. She was confused but flattered.
I know a few people who've done this. When they got married they decided they didn't like either last name so just chose a new one. In one case it was the guy's online handle - which was also a normal last name. In the other case it was a name from their favourite movie.