The name "Thespesius" means wondrous one. Leidy avoided using the suffix "saurus" in the genus name because Vandiveer Hayden had claimed the bones came from a layer from the Miocene so there was a chance that the animal would turn out to be a mammal, though Leidy himself was convinced it was a dinosaurian. "Thespesius" turned out to be a dinosaur. The specific name "occidentalis" means "western" in Latin.