There are a few options for synonyms for the name "Royal Anthropological Institute." One possibility is simply "RAI," which is often used as an abbreviation or shorthand for the institution. Another option is to use the more general term "anthropological society" as a descriptor for the RAI and similar organizations, which focus on the study of human society and culture. Additionally, the phrase "royal institute of anthropology" could be used as a variation of the formal name, emphasizing the institution's focus on the scientific study of human beings and their behavior. Overall, there are several ways to describe or refer to the Royal Anthropological Institute and related organizations.