John is called the savage because he grew up on the reservation in New Mexico where all the "savages" live. Because of that, his ways are really strange in the eyes of the "civilized" people.
His childhood was totally painful. All the Indian women hated his mom because she acted (in their opinion) like a whore (she had the values of "civilization"). None of the kids liked him because of that as well.
He feels he is bound by the laws of the society where he grew up, though. He believes in their morality and the morality he has picked up from Shakespeare plays.
So he is an outcast in two societies, which is why he ends up killing himself, I believe.
In the book A Brave New World John came from the outer region. He lived on an Indian reservation all of his life. To people who are living in the controlled society his ways are very different. He is not like them so they refer to him as the savage.
In truth this is ironic because humanity in the new world is far more savage than John's behaviors. John is a thinker and spiritual. However, his self-flagellation and drinking of potions to purify himself are seen as savage acts. It is his later involvement with some of these acts that causes him to end his own life as he sees them as being wrong.