The only official name change I've done was for my social security card. When we were in the US for Christmas, I went to the DSS office near my mom's house and showed them my marriage license (married name, obviously) and my passport (maiden name). They sent the new card to my mom's house about a week later.
On my SS card, I'm Lola Ellen Married. In my passport, I'm still Lola Ellen Maiden. At work, I'm Lola Married. On my UK bank account and credit cards, I'm Lola Ellen Married. On my US accounts, I'm Lola Ellen Maiden. For my UK drivers license, I'll send in my passport and marriage certificate, registering as Lola Ellen Married.
I don't plan on changing my name in my passport because it's not really neccessary. We book my flights in my maiden name and my spousal visa shows that I'm the spouse of Richard Married, if that info is needed. I'll probably change it when I renew my passport in 2008.
I figured the social security card was the biggie as I wanted to make sure that the name associated with my SSN was the same as my name at work (and thus the name on my payslips and P60) for tax purposes.