Changing name on UK visa and US passport

Hi!

I am a recent newlywed and need to start changing my name on all my documents. I have a Tier 1 Partner Visa, and a US Passport. My question is:

How do I change my name on my Visa? I would probably have to start with my passport??

If anyone has a website with info, or any knowledge on the subject...it would be greatly appreciated.

Thanks, Sofie

Yes you have to do the passport first.

You do your passport as a renewal thorugh the Embassy in London:
http://www.usembassy.org.uk/cons_new/acs/passports/marriage_namechange.html

As far as changing your name on your visa, you don't acutally HAVE to if you don't want to pay UKBA another £165:
http://www.ukba.homeoffice.gov.uk/while-in-uk/transfer-visa-to-passport/

You do not need to transfer your residence permit to your new passport. If you choose not to transfer your permit, you should carry both your old and new passports when you travel to the UK - this will prove to our immigration officers that you have the right to be in the UK. If you cannot produce your residence permit when you arrive at our border, you may not be allowed to enter the country.