Pan (Faunus in Roman)
You are referring to Faunus, whose Greek counterpart was Pan. He is the archetype from which we get Satyrs.
No. A goat cannot become a God, but can be godlike.
It was named after a roman god named "The SATYR" A goat-legged half-man with horns and pointed ears.
The Greek god of nature, and the wild was Pan. He was a creature known as a satyr. His Roman counterpart was the god Faunus.
Pan is one of the most famous Satyrs. He was god of shepherds, flocks, mountains, hunting and music.
The Greek god Pan
A Roman nose on a goat refers to a straight or slightly convex profile of the nose, similar to the appearance of a Roman statue. It is a common feature in some goat breeds, such as LaMancha and Boer goats.
She had a goat skin
Pan
You're thinking of Faunus, but he wasn't a shepherd. He was the Roman god of forests, plains and fields. He was conflated with the Greek god of shepherds, Pan, who was often depicted with those same goat-like features (though he did not originally have them).
A half-goat deity is a mythical being that is part human and part goat in its physical characteristics. One well-known example is the Greek god Pan, who is depicted with the upper body of a human and the lower body of a goat. These deities often represent nature, fertility, and the wild aspects of the natural world.