Pamela Landy (Joan Allen) tells Jason in the end that his real name was David.
Jason remembers his first job was killing a couple in a hotel room. He only meant to kill the husband but the wife was there too so he killed them both and made it like the wife killed the husband, then committed suicide. He re-visited the hotel room and remembered what happened. Then later, he went to the couple's daughter to apologize and told her the truth, that he murdered her parents so her mom didn't kill her dad.
Julia Stiles' return was only for Jason to capture because she was only one that he recognized from last time so that he could ask her questions about what was going on and why he was a target. Julia then cried, thinking he might kill her and said all she knew, which wasn't much anyway.