I stated 'personal reasons' as well. Including when I had to go everywhere to change my name (DMV, University, etc) they would sometimes ask for the reason. Only twice, I think, did someone get too nosy; I remember one woman who said, "Oh, did you get married?" Me: "No, I did not." Her: "Oh, why would you change your name, then?" Me: "Personal reasons." Her: "Oh, really? Why?" Me: *incredulous look* "Personal reasons." Her: *huffy*
But generally it's the best answer to give because it makes it clear to nearly everyone that it's none of their business, and it's completely legitimate.