For everything other than your passport and visa, you can just start using your new name in the UK... you don't have to do anything official, you just need to contact the various companies and change your name with them, such as your bank, utility companies, council tax, store cards etc.
You ONLY need to change your name on your BRP IF you decide to change your name on your US passport... because the name on your BRP MUST match the name on your US passport at all times. You have 3 months from changing your passport name to apply to change your name on your BRP, or you can be fined £1,000 and have your visa curtailed.
So, for your passport and BRP, you have 3 options:
1.
- Change your name in your US passport now ($110, takes about 3 weeks)
- Then change your name on your BRP (£161, takes up to 8 weeks and requires filling out an online application and redoing biometrics).
OR
2.
- Do nothing and keep both your passport and BRP in your maiden name.
You can still use your married name for everything else in the UK, but you'll need to make sure you book all travel in your maiden name.
OR
3.
- do nothing for now, and then in the 3 months before you apply for ILR, change your name on your US passport.
- then apply for ILR in your married name.
The new BRP will be issued in your married name and you don't have to worry about changing your name on your current BRP