As far as I can tell, it's no more complicated than that as long as it is a name change by marriage and you have a marriage certificate. You have to send in your old passport and your marriage certificate in order for them to make it out in a new name, but I had no problem with it. I was worried because I just wanted to add my married name and keep my maiden name as another middle name and had read somewhere that you needed a court order to do that, but I didn't. The marriage certificate is all I have needed to change banks, credit cards, social security, voter registration, and in the UK national insurance and council tax, etc. The only thing I haven't been able to change yet is my US bank account and my US driving license because they said I need to go in person with my marriage certificate, so I'll do that on my next visit home.