satyr is what it is in english... though some call them "pan" because they play the pan flute
Pan, in Greek mythology, is the god of the wild, shepherds and flocks, nature, of mountain wilds, hunting and rustic music, as well as the companion of the nymphs
. His name originates within the Greek language, from the word πάειν (paein), meaning "to pasture." He has the hindquarters, legs, and horns of a goat, in the same manner as a faun or satyr. With his homeland in rustic Arcadia, he is recognized as the god of fields, groves, and wooded glens; because of this, Pan is connected to fertility and the season of spring (thus the erected...) . The ancient Greeks also considered Pan to be the god of theatrical criticism. So a satyr, or a faun, is not Pan... but Pan, is
As for the centaurs, the ancient Greeks believed to be an actual race of people living in central Greece.
Excellent customs Baron!