I don't believe that the dog has a name. It is always referred to as "the dog." Even when, towards the end, the man is trying to get it to come to him so that he can kill it and warm his hands inside the dog's body, he doesn't use any name or even a soothing tone of voice. The fact that the dog does not have a name would make it seem more of a wild animal, closer to its wolf ancestors. And that seems to be what Jack London is trying to emphasize: that the dog still has the instincts of a wolf that is native to this incredibly cold, pitiless environment.
If the question were to read: "How would giving the dog a name change how you feel about this character?," then it would seem that the answer would be that a name would have a sort of "civilizing" effect, both on the dog and on the reader's impression. A name would make the dog seem more domesticated. Personally I like the dog better as he is. He belongs to a brutal man but he retains some of the dignity of a wild wolf. He knows a lot more through his inherited instincts than this ignorant, greedy, ruthless Chechaquo. He has no more love for the man than the man has for him.