In the past, it was always recommended to change your name on your passport/visa just before applying for ILR (or any other visa), as it was easier and cheaper than doing it afterward... or at least, it used to when BRP cards were still issued, as you would need to apply for a new BRP card in the new name. Now that everything is online, it's a bit different.
The reasoning was:
- If you changed your name on your passport, you had only 3 months to also change it on your visa/BRP card, or you could be fined £1000 and possibly have your visa curtailed.
- However, it would cost about £150 to change it on your BRP, would involve submitting another application form and doing biometrics again... and it could take several months to be issued.
- But, if you changed your name on your passport within the final 3 months before applying for ILR, you could simply apply for ILR in the new name and your BRP would be issued in that name... thus saving yourself time and money to change it on your BRP card after you received your ILR.
- Also, you have to apply for UK citizenship in the exact name in your non-UK passport, so if you wanted to be able to apply for citizenship in your new name, you already needed to have your passport and visa in your new name... so again, doing it before ILR made things easier.
If you already have ILR and/or UK citizenship, obviously, the above reasoning is all irrelevant anyway, as you won't be applying for any more visas.
Now, that BRP cards are no longer issued the process is:
If you have ILR (but not UK citizenship):- You can just update your details online here: I think it's easier now that everything is online, because you can just update your details here:
https://www.gov.uk/change-circumstances-visa-brpIf you have UK citizenship:- you will need to apply to change your name in both your US/non-UK and UK passports