My father was adopted as an infant. He was able to learn of his mother's name from court documents. She lived close to my family's home -- I often rode my bike past her neighborhood. She gave a few possible names as fathers, so my dad had his DNA tested. I am still learning (a lot) about DNA research.
I watched a video here: http://www.genealogyjunkie.net/dna-tips-tools--managing-matches.html that explained many details about DNA tests and finding common ancestors. I highly recommend it.