you are handling out lot of Information to the merchant.
If you don't trust the merchant with your address, then why are you buying something from him?
Data leak can happen anywhere whether I trust the merchant or not. How good and secure system you create, Social Engineering will always going to be big threat.
I don't think such kind of services exist, but you can have a P.O.Box rented so that you can say the merchant to ship to your box. You can be anonymous but it's not completely possible.
1. Not everybody will able to send to PO box.
2. I guess, you are responsible to pick the articles from PO box, so you are losing the benefit of home delivery.
It is not just about PO box only, it is just the tip you see. Actual problem is many site require "phone number " also. To be fully anonymous I guess ,lot of other services might be needed.
What about Amazon locker points?I think that they were a solution for this problem.
Nope, They are supplier/Merchant here. They know to whom they rented that locker.