A person who is obsessed with skulls is typically referred to as a "skull enthusiast" or "skull collector." There is no specific term in the English language for someone exclusively obsessed with skulls, but depending on the context, they might be described using various related terms, such as "skull lover," "skull aficionado," or "skull fan." Keep in mind that the term used can vary based on the intensity and nature of the person's interest in skulls.