What is the importance of the names characters have in Green Grass, Running Water?

The names that King has chosen for his characters, particularly the traditional indigenous names, are very symbolic of the characters themselves and their position in life, especially in regard to their identity as indigenous peoples. Charlie Looking Bear for example is a man who, like his father, is perfectly willing to sell his own cultural identity in order to make profit, even though he discovers how shortsighted this is when he is used by the company behind the dam because of his ethnic identity. As his name suggests, he is a man who is concerned with appearances above all else, and his lack of character is something that gives Alberta real concerns when she considers pursuing a relationship with him.

Eli Stand Alone, on the other hand, is a character whose one-man battle against the dam company leaves him literally standing alone, facing a force that has so much more money and resources than he does. Eli's background and his relationship with his cultural identity is explored through his marriage to Karen, and the way that even though his wife was deeply respectful about her husbands roots, he was ashamed of his identity and did what he could to avoid going back to home and seeing his family. Note for example what he thinks as he is about to head back to the Sun Dance:

As Karen worked her way through Toronto traffic, Eli tried to think of what he was going to say to his mother. It had been over twenty years since the last visit. He had no excuses, no good reasons why he had stayed away so long. Even Karen's illness couldn't cover over his absence.

Eli is a man who is deeply divided, clearly ashamed of his cultural heritage, and therefore his act in "standing alone" to oppose the dam that would destroy his family home is symbolically a battle that allows Eli to try and work out who he is and to come to terms with his ethnic identity. It is a battle that he fights by himself, as his name suggests.