my name means horse…
It really means a spring or a well most likely, according to Hesiod.
The poet Hesiod connects the name Pegasus with the word for “spring, well”, pēgē: “the pegai of Okeanos, where he was born;”
Pegasus (Greek Πήγασος/Pegasos, Latin Pegasus) is one of the best known fantastical creatures in Greek mythology. He is a winged divine horse, usually white in color. He was sired by Poseidon, in his role as horse-god, and foaled by the Gorgon Medusa.1 He was the brother of Chrysaor, born at a single birthing when his mother was decapitated by Perseus. Greco-Roman poets write about his ascent to heaven after his birth and his obeisance to Zeus, king of the gods, who instructed him to bring lightning and thunder from Olympus. Friend of the Muses, Pegasus is the creator of Hippocrene, the fountain on Mt. Helicon. He was captured by the Greek hero Bellerophon near the fountain Peirene with the help of Athena and Poseidon. Pegasus allows the hero to ride him to defeat a monster, the Chimera, before realizing many other exploits. His rider, however, falls off his back trying to reach Mount Olympus. Zeus transformed him into the constellation Pegasus and placed him in the sky.
Pegasus render by rainyday