The correct answer is "He alluded to her without mentioning her name." This is because the word "alluded" means to suggest or indirectly refer to something or someone. In this context, it implies that he mentioned or referred to the woman without explicitly stating her name. On the other hand, "referred" simply means to mention or direct someone's attention to something or someone, without any indication of indirectness or suggestion. Therefore, "alluded" is the more appropriate word choice in this scenario.