PayPal FAQ:
Do I need to have a registered business in order to have a PayPal Business account?
No, you do not need to have a registered business. You can still get a PayPal Business Account under your personal name.
What name should I use for my business when I set up my PayPal Business account?
Your PayPal Business name should be your own name and it should match the name of your bank account.
This is to ensure that transfers and withdrawals will be able to go through successfully between your PayPal account and your bank account.