It’s 3 months from receiving the new US passport.
The name on your BRP must match the name on your passport at all times. If you change your name on your passport you have 3 months from receiving it to apply to change your name on the BRP, or you can be fined £1000 and have your visa cancelled.
However, you do have to go through the whole online application submission and biometrics process again to update the BRP, and it can take several weeks for it to be processed, plus it costs £200 to do it!
So, to make things easier, it’s best to update your US passport in the 3 months before you submit your ILR application… so that instead of having to change your name on your current BRP, you can just apply for ILR in the new name and get your next BRP issued in that new name.
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