Rie Tamada and GAMI, the tag team known as ReDragon in Aja Kong's ARSION.(and later, Kyle O'Reilly and Bobby Fish, reDRagon in Ring Of Honor)
Big Japan's Death Match Dragon, Ryuji Ito
"American Dragon" Bryan Danielson, one of the few non-Japanese to ever win that honor in Japan.
Dragon Kid and his nemesis Darkness Dragon
Dark Dragon, who fought the "King Of Monsters" Blue Dragon and later, Ultimo Dragon (came before Blue Dragon but sort of inherited his nemesis, sort of not as one of his Dark Dragons turned out to be long time foe Hajime Ohara)
Puerto Rican legend of the AWA and All Japan Womens Pro Wrestling "La Tigresa" Irma Acevedo, as well as her more terrifying successor simply known as La Tigresa in WWC and IWA Puerto Rico (not to be confused with Mexican Tigresa del Norte).
Tiger Mask and his many successors such as Tiger Dream and Extreme Tiger as well as evil knockoffs, such as Black Tiger and Masked Tiger.
Early on his career Chris Jericho had a number of lion-based names and nicknames, which fit well with his long blond hair. He hasn't gone by any of those names in years, even since before he cut his mane short...but his version of the springboard moonsault is still called the "Lionsault".
Tigre Universitario and Mini Tigre Universitario in IWRG
Sable has a leopard screeching on her entrance theme.
Canines tend to be for tag teams and trios, due to being social animals
Bulldog Mallory back in the 1930s
Butcher Vachon and Mad Dog Vachon in the 1950s
Legendary CMLL luchador Perro Auagayo. Perro Auagayo Jr. would go on to found the Card-Carrying Villain stable Los Perros Del Mal, which would causes mischief in CMLL, splinter fed AAA and then start its very own promotion with its own "evil" title belts.
The Havana Pitbulls Ricky Reyes and Rocky Romero, starting in Ultimate Pro Wrestling, who were in turn part of the Rottweiler stable.
Foxes for 21st Century Fox, obviously.
Bolo The Red Bull Dog of New Wrestling Generation, WWC and IWA Puerto Rico
Jesse Neal is known as "The Dog Of War", which is an old nickname for the USA Army soldiers, which he was.
Belgian and Netherlands promotions such as Free-Style Championship Wrestling have Amsterdam Bulldogs Vito Toscani and Wesley Croton.
The Ring of Honor tag team of Eddie Edwards and Davey Richards call themselves "The American Wolves," referencing their ferocity and team mentality. AR Fox (which might be enough to count on its own) formed the African American Wolves with ACH in Pro Wrestling Guerilla.
Raven Hiroka, Pricesa Blanca and Princesa Sugeith: Las Zorras of CMLL.
Mexican tag team Los Perros del Infierno, Perro Salvaje and Demonio Azteca out of Cuernavaca, Morelos.
The Shield are collectively known as "The Hounds of Justice" and dogs feature prominently on their gear.
"The Lone Wolf" Baron Corbin
Snakes are a natural, at least when one remembers wrestling is supposed to be a grappling sport.
African Wrestler(specifically, Democratic Republic Of Congo) Bob Elandon, also known as N'boa the snakeman in the 1950s.
Penny Mitchell, who briefly wrestled under a mask as The Spider Lady before her manager, The Fabulous Moolah, stole it.
Infamous WCW wrestler Arachnaman
Mariko Yoshida, after phasing out her high flying in Arsion but keeping the exotic submission holds of lucha libre, as well as adopting catch as catch can tactics, took up a spider web motif to drive it home.
Football player turned pro wrestler Nate Webb, for a different kind of "catch".
The Los Angeles based Scorpio Sky, especially when he still had his mask
Rey Escorpión of Rush's Los Ingobernables, and his brother Black Scorpió
Black Man of Los Tres Fantasticos had previously wrestled as Spider Man and La Gacela. The Spider Man gimmick in particular was taken up by many after he phased it out due to Fantasticos' runaway success, the Gacela gimmick had a much more dramatic end when the mask was taken by Super Dolphin in a wager match, and as such wasn't as widely adopted.
Big Van Vader used to be associated with bulls before he got his more famous gimmick associated with elephants.
Chris Benoit was known as the Rabid Wolverine, and had also wrestled as The Pegasus Kid.