What does Rip Van Winkle's wolf represent?

Wolf is the name of Rip Van Winkle's dog. In many ways, I'd suggest that Wolf represents Winkle's life back in the colonial era, lost forever after his long sleep, and the changes that have reshaped the former colonies, now United States, in that time. After all, Wolf plays a role on both sides of that divide.
Before Winkle's sleep, Wolf is Rip's loyal companion and joint-sufferer under his wife's force of personality. When Rip Van Winkle awakens from his sleep, it is to find a radically changed world, which he has severe difficulties re-assimilating into. This difficulty is reflected in his encounter with his dog—or at least in his encounter with what he believes to be his dog. He finds that Wolf has changed dramatically in the years where Rip was gone. The dog, now described as "half-starved" and a "cur," shows hostility to Rip.
Wolf's change reflects the larger changes which have shaped this transition from the colonial era to the post-Revolutionary War United States. Rip Van Winkle's past has been lost to him, much like the Wolf he remembers.