Mohammed Amer was 20 and starting to get some attention as a stand-up comic when Islamist terrorists attacked the U.S. on Sep. 11, 2001. At first, Mr. Amer’s dreams seemed doomed. Some friends told him it was time to change careers; others worried for his safety. A few tactfully suggested he might still seem relatable and get some laughs if he simply changed his name and stopped talking about being a Palestinian Muslim refugee.