Certain types of bank accounts can help you stay (more or less) It is possible enjoy some privacy if you have the right accounts set up. It takes. How do I open an anonymous PayPal account? you want to do that, paypal will never allow you to add someone else bank account or anonymous accounts. If you open a personal bank account, the bank secrecy will protect your privacy at a certain level, but to get % Anonymous Offshore Bank Account, you will.