Define private, you walk in public in front of security cameras wearing your face in public. your face is now public information.

Your name is on your mail, your census, your driving licence, you provide your name and address to companies all the time. your name and address is now public information.

If someone can tie your public face to your public name then thats public information.

you dont like it, get a PO box and wear a mask all the time.

In many countries including the US, yes. If the right mixture of you, the company, and your friend are located in or deal with Europe or similar places, possibly not, but it very much depends on the details.