Santiago taught the boy to fish, and the boy loves him. That’s what Hemingway tells us, and that’s about how he tells us, too. There’s no confusion, and we don’t sit around wondering what’s the deal with these two. The boy is the one human companion that the old man has, and he remarks (internally) on how grateful he is to have the company when he comes back. Most important, however, is the fact that the boy respects the old man. He believes he is a great fisherman, age be damned, because he knows Santiago’s skill and prowess.
Why does the old man repeatedly wish the boy were there? That’s an interesting question. At first, it seems to be because he needs help, what with the ginormous marlin and all. But you could also argue that it is for companionship, that the old man is lonely. Or you could say he wants someone to bear witness to his feat.