Another Americanism I've thought of, that's at least used in the midwest and south, is calling the Woodcock 'bogsucker'.
I've dusted off my old used copy of "The Dictionary of American Bird Names" by Ernest Choate, and have found, among other things:
ACCENTOR: Local name for the Ovenbird, for the penetrating two-syllable song in which the first syllable is accented: TEACH-er, TEACH-er, TEACH-er
BALDPATE: American Widgeon (the white forehead patch resembling baldness)
BASKETBIRD: Baltimore or Northern Oriole, whose nest resembles a basket hanging from a branch
BOGBUMPER: American Bittern, probably for its call
BURGOMASTER: Great Black-Backed Gull, for its large, dominating size
CHEWINK: Towhee, for its call
CUTWATER: Black Skimmer, for how its bill is cutting through water as it feeds
GOBBLER: Wild Turkey, for its call
HELL-DIVER: Grebes, particularly the Pied-Bill
LOG-COCK: Pileated Woodpecker
LORD GOD BIRD: Ivory-Billed Woodpecker, supposedly because its rare sighting and large size would cause people to exclaim, "Lord God, the Bird!"
MUD-HEN: A coot. And there's a baseball team in Toledo, Ohio that calls itself the Mudhens!! Klinger would wear their jerseys on M*A*S*H
RAIN-BIRD: American Cuckoos
REED BIRD: Bobolink, for where they congregate, especially in the Middle Atlantic states, before fall migration
SAWBILL: Mergansers (divers) for their serrated bills
SNAKE BIRD: Anhinga (for which I've also heard WATER TURKEY)
THUNDER PUMPER: American Bittern, for its call
TIMBER DOODLE: Still another for the Woodcock
WHISKY JAY: Common, local name for the Gray Jay