Could knowing your DNA genetic information become a privacy issue for mothers who put their children up for adoption?

I just thought of something. If a child was put up for adoption and decides to have their DNA tested, does this become a privacy issue? What if the birth mother didn't want anyone to know she had a child? What if the father already had a family and doesn't want the complication of a long lost child popping up? Because if you are told of any potential match, it wouldn't take much to find your parent. Something to think about.