the above assumes that you have a credit facility with your bank that reports to the credit reference agencies [ experian, equifax].
You should change your name with all your creditors, to ensure consistency, and at the very least one of your active credit facilities to ensure the updated name information is recorded in your credit file.
Also on future credit applications you should declare your previous name to the lender, for credit information in that name to be taken into account. A belt and braces approach