I have indefinite leave to remain in uk. Following my divorce, I want to change my name in pport.?

I am permanent resident in UK for over 20 years. I am now divorced and reverted to my maiden name with driving licence and utility bill, bank etc. Now my pport is for renewal and am thinking of changing to maiden name. Would this affect my ILR? Do I need to transfer ILR to my new pport , which is very expensive, instead of just carrying old and new pport for immigration at the airport?