I have never even considered the possibility that the ‘Pan” in Peter Pan is based on Pan the Greek god of nature.
Pan is a figure who recurs through European culture, especialy after the Romantics. But he became a natural and pervasive Edwardian god: a playful wild outdorr hero that never ages, combining in one image the delights of rural and childhood retreat.
Peter Pan, whose horned cap, rural attire and pan pipes are the only remnants of his descent from the Greek centaur, is the most eccentric and the most human of all these creatures. He could not have come about with out the cultural obsession with Pan, but he belongs as much to the popular archetype of the immortal young man which was developing in the 1880s when Barrie was forming literary ambitions.
From Inventing Wonderland by Jackie Wullschlager
Maybe we should reconsider or consider some of our own cultural obsessions.