Species with Multiple Common Names (Competition)

Banggai Cardinalfish - Kaudern's Cardinalfish

Schooling Bannerfish - False Moorish Idol - Poor Man's Moorish Idol - Pennantfish - Schooling Coachman

Red Bass - Twospot Red Snapper - Bohar Snapper - Kelp Bream - Kelp Sea Perch

Pencil Surgeonfish - Dussumier's Surgeonfish - Dussumieri Tang - Eyestripe Surgeonfish - Hawaiian Surgeonfish - Pencilled Surgeonfish - Ornate Surgeonfish - Whitespine Surgeon

Coconut Crab - Robber Crab - Palm Thief

Coral Beauty - Twospined Angelfish

Bluestreak Cleaner Wrasse - Gadfly Fish - Blue Streak - Common Cleaner Wrasse - Bridled Beauty - Cleaner-Fish

 

I’m adding some (mostly North American) fish names:
Alligator Gar: Gator Gar
American Paddlefish: Shovelnose Cat, Spoonbill Cat
Amur Carp: Koi
Atlantic Tarpon: Sabalo, Silver King
Brook Trout: Brook Char, Speckled Trout
Brown Trout: Finnock, Lake Trout, River Trout, Salmon Trout, Sea Trout
Chinook Salmon: King Salmon, Tyee Salmon
Chum Salmon: Dog Salmon, Keta Salmon, Silverbrite Salmon
Coho Salmon: Silver Salmon
Common Dolphinfish: Dolphin, Dorado, Mahi-mahi
Eurasian Carp: Common Carp, European Carp, German Carp, Ghost Carp, Golden Bonefish, Leather Carp, Mirror Carp, Sewer Trout
Freshwater Drum: Gaspergou, Gou, Sheephead, Silver Bass
Grass Carp: White Amur
Guadalupe Bass: Texas Trout
Lake Trout: Lake Char, Mackinaw, Namaycush, Siscowet
Largemouth Bass: Bucketmouth, Green Trout, Largemouth Black Bass
Longnose Gar: Billy Gar, Garpike, Needlenose Gar
Muskellunge: Muskie
Northern Pike: Jack, Jackfish
Pink Salmon: Humpback Salmon, Humpy Salmon
Red Drum: Channel Bass, Grass Bass, Puppy Drum, Redfish, Spottail
Redear Sunfish: Shellcracker
Redeye Bass: Coosa Bass
Smallmouth Bass: Bareback Bass, Bronze Bass, Brown Bass
Sockeye Salmon: Blueback Salmon, Red Salmon
Spotted Seatrout: Speckled Trout, Spotted Squeteague, Spotted Weakfish
Tautog: Blackfish
Walleye: Pickerel, Pike, Wall-eyed Pike
Warmouth: Goggle-eye, Warmouth Bass
Weakfish: Squeteague
White Bass: Silver Bass
Yellow Bass: Brassy Bass
Yellow Perch: American Perch, American Yellow Perch

 

Some more ray-finned fish names to add to the list:
Ara: Sawedged Perch
Atlantic Goliath Grouper: Jewfish
Atlantic Pollock: European Pollock
Australian Salmon: Kahawai
Ayu: Sweetfish
Bluefish: Elf, Tailor
Bluestreak Cleaner Wrasse: Cleaner Fish
Brown Meagre: Corb, Corvina, Sea Raven
China Rockfish: Yellowspotted Rockfish, Yellowstripe Rockfish
Colorado Pikeminnow: Colorado Squawfish, Colorado White Salmon
Crevalle Jack: Common Jack, Jack Crevalle
European Perch: Perch, Redfin Perch
Eulachon: Candlefish
Fallfish: Little Tarpon
False Kelpfish: Marbled Rockfish, Sea Ruffe
Freshwater Catfish: Dewfish, Eel-tailed Catfish, Jewfish, Kenaru, Tandan
Golden Dorado: Dorado, Jaw Characin, River Tiger
Green Sunfish: Black Perch, Bream, Goggle-eye, Green Perch, Rice-slick
Hardhead Catfish: Hardhead, Sea Catfish, Tourist Trout
Huchen: Danube Salmon
Ide: Orfe
Indo-Pacific Tarpon: Bulan-Bulan, Oxeye Herring
Ladyfish: Skipjack, Tenpounder
Largehead Hairtail: Beltfish
Longtail Tuna: Tonggol Tuna
Meagre: Brown Meagre, Corvina
Mulloway: Japanese Meagre, Jewfish, Kingfish, River Kingfish
Northern Cisco: Cisco, Lake Cisco, Lake Herring, Tullibee
Northern Pikeminnow: Columbia River Dace, Squawfish
Norway Redfish: Atlantic Redfish, Golden Redfish, Norway Haddock, Ocean Perch, Pinkbelly Rosefish, Rose Fish
Pollock: Boston Blue, Coalfish, Coley, Saithe
Pumpkinseed: Punky, Sunny, Sun Perch
Regal Blue Tang: Blue Tang, Hippo Tang, Palette Tang, Palette Surgeonfish, Regal Tang, Wedgetailed Blue Tang
Sablefish: Black Cod, Bluefish, Butterfish, Candlefish, Coalfish, Snowfish
Sakhalin Taimen: Japanese Huchen, Stringfish
Silver Perch: American Silver Perch
Skipjack Shad: Skipjack Herring
Skipjack Tuna: Arctic Bonito, Mushmouth, Victor Fish
Snoek: Barracouta
Spotted Sunfish: Stumpknocker
Striped Mullet: Flathead Grey Mullet
Tambaqui: Black Pacu, Giant Pacu
Tench: Doctor Fish
White Crappie: Sacalait, White Perch
Zander: Pike-perch

 

Tapirus terrestris - Brazilian Tapir, Lowland Tapir, South American Tapir [Good thing there are only a few Baird's and no Mountain tapirs on the continent..]
Choloepus didactylus - Linnaeus' Two-Toed Sloth, Linne's Two-Toed Sloth, Unau, Two-Toed Sloth [typically used in the absence of C. hoffmanni]
Suricata suricatta - Meerkat, Suricate [seems to be falling out of fashion], Slender-Tailed Meerkat [possibly used as so visitors believe that these meerkats are different from everywhere else's meerkats]
Nasua nasua - Ring-tailed Coati, South American Coati [unhelpful as most coati species are native to South America, but may be an absentia clause as is above], Brown-nosed Coati
Pseudorca crassidens - False Killer Whale, Psuedorca

 

All I can think of right now is the obvious puma/cougar/mountain lion and African wild dog/Painted dog.