You will need to submit a change of circumstances and provide evidence of your name change, such as a marriage certificate or deed poll.
If you have no official document to prove that you have changed your name, you can provide a letter from a professional person, highlighting both of your names and your date of birth. The letter should be on headed paper if available and should also include the name, address and telephone number / email address of the professional person. However if it is a sensitive subject where no outside bodies have been involved a letter from a family member can be considered.