A New Jersey hospital identified itself on Wednesday as the one that released a man on May 18 who later died of a rare disease that he may have contracted in Liberia. But the hospital, St. Barnabas Medical Center in Livingston, said the man had not told hospital staff of his recent travels until at least three days after he first visited the emergency room — a disclosure that, if made sooner, could have allowed health officials to prevent transmission to others and potentially save him. The man, who has not been identified, died on Monday night of Lassa fever, a viral disease endemic to West Africa and with symptoms similar to Ebola, but far less deadly.