1) Eliminate all shared finances (i.e. bank/credit/debit accounts) immediately if possible. Shared credit cards and joint debt, such as cars and houses, are more difficult to eliminate until your divorce is complete. Your lawyer should be able to give you the best advice with joint accounts/debt.
2) Credit freeze immediately. If you're managing your money correctly, you should know in advance if you need access to credit or a credit check. You can unfreeze for a short period and then refreeze afterwards.
3) Check all three credit reports now to get a baseline before you have any suspicion of any actual wrongful activity. Then start checking your credit report regularly by checking one of the three reports each quarter.
4) Name change is a last resort and probably not very effective. Unless you're moving and cutting all social contacts, he still has your SSN and DOB. He could possibly find your new name via social media/Google if you post anywhere online with your name, especially if you keep several of the same friends online. Your mother's maiden name would only be useful if he were trying to answer security questions for an existing account. It's not usually required to open a new account.