When you make a payment the merchant will see the following:
1. Your name
2. Your shipping address (if you purchased a physical item that needs to be shipped)
3. Your email address associated with the payment
These are the typical pieces of information that are provided. Your address can be kept private if you never buy anything that requires shipping but as most customers are using their PayPal account to make purchases for goods, I don't see that this would be feasible. I hope this helps you and I wish you a great day.