I don't think there's much risk, unless you are trying to keep your name and address completely secret from all potential buyers until you exchange the title for the money in the lobby of your local bank branch.
The Driver's Privacy Protection Act is supposed to protect the release of personal information for a non-permitted use, but it's probably not that hard to get around the law and find out your name and address from the VIN.
But anyone can walk up to your car and read the VIN from the plate on the dashboard.
And it's a legitimate request by the buyer - they won't be able to run a Carfax without the VIN and that's a cheap way for the buyer to gain a little protection.
Some dealer service writers will pull up service and recall records by VIN for potential buyers but most of them are pretty careful not to disclose personal information about the current owner of the car.