For the meantime use your maiden name in all your applications (i.e. bank, national insurance, work, licence) matching to both your BRP and Passport.
I suggest to renew your passport atleast 2 months before you apply for ILR. Ensure your passport will be received before your FLRM expires.
ah so i need to follow what's written on my BRP and passport. thank you so much again for telling me such an important information in order for me to start a new life.