Finding it impossible to change last name and hence file tax

Hi, I moved to UK in June and got issued an NI. Shortly thereafter I changed my last name (I moved to UK after marriage). Because my NI is linked to previous name, I can't create HMRC login to file taxes. I have been trying for several months. I am already aware of your suggested phone number and communication address. I have tried to call repeatedly and when once I was lucky I was asked to send a letter to your correspondence address. It has been 2 months. No reply and no change of name in the system. This is extraordinary. Can you please provide a method that will actually work.

Hi

I'm sorry for the delay in updating your name since you wrote to us - contact us by webchat or post via
Income Tax: general enquiries
and, if we can't update your name for you then, we can confirm the progress of your mail request.

Thank you