Thank you for the opportunity to help you with your question!
Pan is a mythical god who is the head of the Fauns. It is called Pan's Labyrinth in reference to the god faun "Pan". However, when converting the title to English the director didn't want to call it Pan's Labyrinth, but it stuck non the less.
there is no character in the movie called "Pan." the movie, in Spanish, is called El Laberinto del fauno, which means in English The Labyrinth of the Faun. But when the movie came to the US, the producers did not want to call it The Labyrinth of the Faun. So for commercial purposes they changed the title to Pan's Labyrinth (Pan is a greek god, in the shape of a faun). the director of the movie has stated that the faun in the movie is not Pan. so really the title, pan's labyrinth, is only to make more money and sound better than the labyrinth of the faun.
Please let me know if you nea case for torture by michale levined any clarification. I'm always happy to answer your questions.