I just went through an ordeal that I wanted to put out for everyone.
According to PayPal, a change in the Patriot Act now treats PayPal as any other financial institution. You will be required to provide proof of your identity via a state issued ID, proof of address via a bill and proof of your SSN via a copy of your Social Security Card.
Also, unless you have a business with a Federal EIN, your FULL name will be displayed for any PayPal transactions.
Your only option, if you do not want to provide this information to them, is to close your account.
Just an FYI for those that use PayPal.