With the city name Buffalo, it is theorized that Buffalo roamed that area until the mid 1700's. And a creek there was named Buffalo Creek. So that is probably where it got its name.

Personally I think a team name needs to denote a body of some sort. Jazz is a type of music. How can a player be a Jazz? How do you picture what a Jazz would look like? A giant saxophone? A Yankee you'd picture a guy in an Uncle Sam outfit, a Giant is a giant, and so forth. Naming something after an element or a vague embodiment of nature is silly. I'll even rip on the Mets. Whats a Metropolitan? A guy in a business suit? That's dumb too.