Symbolism, Imagery, Allegory
Okay, so Surrender is Gabriel's dog and a gift from his dad. He quickly becomes Finnigan's pal, though, since they're more alike—the dog likes to hunt and roam, just like Finnigan does, and has a penchant for springing himself violently on other people's property. Finnigan sets fires, while Surrender gobbles chickens.
But this pup doesn't symbolize friendship or loyalty in the ways we might typically think of dogs doing; no, this dog is all about his name, which means: "to allow something […] to influence or control you." And we don't mean to just let the puppy love wash over you.
After Surrender attacks a neighbor's goats, Gabriel's father forces him to kill the dog. Terrible, right? And adding to the terribleness, of course, is the fact that the dog was a rare gesture of kindness from Gabriel's father. So in forcing his son to kill his dog, he's also symbolically asking him to destroy this gesture and any positive meaning he may have attached to it. Ouch. And since Gabriel is powerless to exercise any control over the situation, well, you might even say he has to surrender to his father's wishes.
This surrendering, though, begins a much bigger process. It sets rage boiling in Gabriel's belly, putting in motion the beginning of the end of his need for Finnigan. This anger and hurt over being forced to kill his dog factors into Gabriel's subsequent snap that results in him murdering his parents. He is so done with these people, yes, but more than that, it begins to become difficult to insist that Finnigan is outside of himself as the darkness within Gabriel grows. It's almost like an eclipse—Gabriel starts to surrender to his own darkness.
And surrendering to killing Surrender is what gets this ultimate surrender going. Say that five times fast.