I have little doubt some of these companies do de-anonymization themselves (or through a third party). I use a PO Box for all my mail, yet I somehow get ads delivered to me based on my interests and recent purchases in my name to my residential address. I've literally never purchased anything using my residential address, I have zero mail sent here intentionally.
Do you receive mail to both addresses under the same or any name? Is it required to have the name field populated to receive mail to your physical or P.O. Box?
Oh another point this reminded me of: I go by Alex (to the extreme that it's on my bank accounts and credit cards) but all the ads have my full name Alexis. When I google my full name in quotes, all of the results are data brokers.
Full name isn't required, I've received mail to my PO box with my first name only, last name only, initials, etc...
My residential address is used so infrequently that my cousin remembers my PO Box number but had to recently ask for my street number to visit.