McDermott's father's third wife was playwright Eve Ensler (author of "The Vagina Monologues"), who legally adopted McDermott when he was 15 and she was 23. She has since divorced his father. Ensler, with whom McDermott has remained close, encouraged him to pursue an acting career, and began writing roles for him into her plays. After Ensler suffered a miscarriage, he took on the name Dylan, the name planned for her unborn child. He then graduated from the Jesuit-run Fordham University with a BA in 1983, as well as studying under Sanford Meisner at the Neighborhood Playhouse School of the Theatre in New York City, the same year as Allison Janney.