Shih Tzus are a breed of dog originating from Tibet, and their name comes from the Tibetan words "zhi" (lion) and "ts'a" (dog), meaning "lion dog." This refers to their appearance, as they have a long, flowing coat and a proud, lion-like demeanor.
It is possible that someone might call a Shih Tzu a "Chrysanthemum dog" due to the way their fur can sometimes be styled, resembling the petals of a Chrysanthemum flower, but this is not a standard or recognized name for the breed.