Personally...
I wouldn't worry about it.
The choice to let the buyer make the call is the best option.
Because...
Anonymity barely exists anymore. If I have your name and town ( Fairfax Station, VA) I can not only find your address but see where you live with Google Maps and possibly find your picture. And I can do it in less than 10 minutes without any special software. Just knowing you're a retired Colonel over the age of 70 makes it that much easier.
Try it yourself.
I scared the crap out of a guy in 2010 by tracking him down with nothing more than a photograph of his truck, the name of the city he lived in, and an email address (which didn't give away his name).
The truck was posted for sale, but an email to the address listed as the contact in the ad came back with an "On vacation until XX date" auto-reply.
But I was in a hurry to get a look at the truck.
I spent about 25 minutes working the Google-Fu to come up with a name. That lead to an address. The address was referenced on satellite imagery, which showed what appeared to be the same truck in a location that made sense for the background in the provided image. Having the correct address meant I could dig up a bit more.
By the time I was done - using free tools, mind you - I knew the guy's phone number, employer, wife's name (second wife), tax status on his home, and that he had filed Chapter 11 in 2003.
Today, it's even easier, with sites like
Pipl.