Name change

Hi there,
Sorry if I didn’t choose the right place to post my question.
Recently changed my name in Bulgaria. Now I want to update my new name here in Uk where I’m living almost 10 years. I have proof from Bulgarian court which I will translate in english and legalise.
My question is, can use this document for prof to change my driving license, bank account, NIN and other institutions.
Thank in advance

You can change your name in the UK via deed poll. Remember that if you also hold UK nationality and passport, the passport office will only issue a new British passport with your new name only if you can show that you legally changed your name in your Bulgarian passport too.

https://www.gov.uk/change-name-deed-poll