Neal had no idea his name was Neal until Ellen TOLD him it was. He was THREE when his name was changed to Danny. I doubt he would have had any coherent memories of his true last name. As far as he was concerned, his father was dead. All of his identifications would have the name Danny Brooks, birth certificate, social security card, ALL his school records . . . this is a pretty big plot hole for me. I HOPE they're able to fill it in a plausible way. Just have to keep fingers crossed.