Changing last name after marriage in US--Lives in UK

I am just wondering how I go about changing my last name after marriage.  I was married 2 years ago in the US(at the time living in the US).  My husband and I moved to the UK a few months ago and I've decided for an anniversary present, to change my last name.  How do I go about doing this.  We are living in the UK permanently now but still have assets in the US(bank accounts, social security num, etc).  Would I change it in the US first, then in the UK?  Thanks for all of your help .

In the UK you just tell everyone that you'll be going by $MarriedName.  You may need to show your marriage certificate to people like the bank but most people (dentist, vet, GP office, work) just took my word for it.

Unless your passport was issued within the last 12 months you will have to pay for a new one.  If you want your visa in your new name in your new passport you will also need to pay for a new one (seriously). Otherwise you would carry your new MarriedName passport along with your old passport with the visa and show both. As for the rest, I've not done it so I haven't the foggiest idea 

I havent changed my name in my passport either but I am considering doing so before I apply for ILR next summer.