"del mar" is a contraction of "de la mar", Spanish for "of [or from] the sea". I took it to be an old Spanish name, because Annie Proulx says in an interview somewhere that the people she's writing about are "autochthones", which I had to look up, not being familiar with the word. It means an "original or indigenous inhabitant of a place; an aborigine". As the Spanish were the first European settlers in the American west, I drew that conclusion. Does someone have a different theory?
Actually, del Mar is not a contraction of de la mar. It's just another way of putting it. El mar o la mar are both correct. So you can either say del mar o de la mar. I, for one, never ever refer to the sea as la mar, I call it el mar. "La mar" used to be a spanish fishermen's slang, because in Spanish when you're going sailing and you want to be poetic about it, you say "hacerse a la mar". But "la mar" is now so widespread that the Royal Academy of the Spanish Language accepted it as a correct way to refer to the sea. However when you speak in plural it's wrong to say las mares. The correct way is LOS mares. And when you refer to a particular sea, for example The Red Sea or The Caribbean Sea, you say El Mar Rojo or El Mar Caribe, never La Mar Roja o La Mar Caribe, that's wrong.
Also, Del mar is a spanish last name (though not very common) as well as a woman's middle name. For example: Maria del Mar or Rosa del Mar.