No doubt about it. Lots of renters are curious about the kind of person they are renting from. Some are excited to be renting from an individual because they have had bad experiences with management companies in the past. Other people like renting from an individual because they can take advantage of this person when the management company won't let them.
Like anything else, the trick is finding out which they are. I only work in my small town, and there are about three or four of us that control most of the rentals. Five minutes on the phone solves a lot of problems. By the same token, I go above and beyond to make sure expectations are known up front and do the maintenance on my properties it taken care of. It is a small town. Unfortunately, it is likely that a tenant has children that go to school with my children, or we go to the same church, or we went to school together. Lots of them know where I live, even though I operate through a PO Box.
When I get this question though, I am vague with the answer. For instance, maybe you could say; well, I just own the five here in town. You might own another hundred in the next town, but they don't need to know that.