Three-headed dog is a unique term that has distinctive connotations in mythology and pop culture. However, if you want to explore alternative terms for this creature, there are a few options to consider. In Greek mythology, the three-headed dog is often called Cerberus. This name is now widely used as a synonym for three-headed dog. However, you can also go for "Tribeast" or "Thrithan" as potential alternatives. Other synonyms for three-headed dog might depend on the context, such as "guardian" or "protector." Overall, there are plenty of options that can be used as alternatives for this mythical and intriguing creature.