If the tax return contained direct deposit information (your bank account number and routing number, or the account number and routing number for a pre-paid debit card) you should contact the bank or card issuer to change the account number. I don't know that you need to change other accounts that were not included.
Certainly, you can contact all your banks and credit cards and set up account alerts to text or send emails for certain actions (such as, card not present purchase, purchase over a certain $$ amount, foreign purchase, etc.). Naturally you will get some alerts for your own activities like Amazon.com purchases and so on.
