When I got GE the CBP agent suggested that, when the time came, I consider moving my maiden name to my middle name so my new name would be: First Maiden Married. He said it made it easier if I couldn't change all of my documents of FF programs at once. So far, so good! (I've been married for 14 months and my name has been officially changed via SS admin for 9 months.)
Rules are different state by state, but I had to change via SS first, then have my DL changed. I traveled for several months with my new ID (First Maiden Married) on tickets that were under my old name (First Maiden). The first few times I kept my passport with me with my old name, but I never had an issue. I did make sure my passport was updated along with those FF accounts before traveling internationally, but I still haven't changed every account over (wanted to wait for US and AA to merge).
Good luck, changing get my FF and hotel accounts was the biggest pain in the process!! Lots of faxing documents (who still faxes??)