In Spanish, faun is fauno. Why did the English version insist on making the faun into Pan himself? Who was Pan? Why include the god of forests and nature?
According to Guillermo del Toro, the use of the word Pan in the non-Spanish versions was just a translation issue. It's not just the English version that has this mistake; the French and German translations also make it. Since he wrote his own subtitles, it was del Toro himself that chose to use the word Pan, but he's has admitted that the name is not accurate.
He likely chose Pan because he is the most well-known faun-like creature in classical mythology (even though it's the wrong mythology), so a name that viewers would identify with. But, The Faun is not Pan:
And the character of the faun is essentially the trickster. He is a character that is neither good nor bad. He's a character ... that's why I chose a faun. Not "Pan." Pan is just the translation, which is not accurate. It's a faun, because the faun in classical mythology was at the same time a creature of destruction, and a creature of nurturing and life. src