Changing your name by deed poll does not affect your credit score or erase your credit history. Your credit file is linked to your identity, not your name, primarily via your date of birth, address history, and financial account details. When you update your name with your bank and other financial organisations, the credit reference agencies (Experian, Equifax, and TransUnion) update their records accordingly through the data they receive from lenders. Your credit score carries over into your new name.
The key practical step is to update your name with your bank first, as banks are the main data providers to credit reference agencies. Once your bank has updated your records and reported your new name to the agencies, your credit file will be updated the next time that lender submits data (typically monthly). You can also contact the credit reference agencies directly; Experian, Equifax, and TransUnion each have processes for updating personal details. In practice the bank update usually flows through without needing to contact the agencies separately.
One thing to be aware of is the period between changing your name with some organisations and not others. If your bank account is in your new name but your electoral register entry or utility accounts are still in your old name, a credit check during that window may show a name mismatch, which some automated credit scoring systems flag. The solution is simply to work through your updates promptly. Keeping your electoral register, bank, and utility accounts consistent matters more for credit purposes than the speed of any single update.