Names for polydactyl cats usually revolve around their extra digits, so names like Miss or Mr. Toes and Mittens are common. Others correspond to famous polydactyl cats such as President Theodore Roosevelt's cat Slippers.
Big Foot, Digit, Tom Thumb, Footz, Toe-ny and Footzie are all names related to feet and the fact that the polydactyl cat has extra toes. Da Jiao is Chinese for Big Foot. Catcher and Katsha refer to the fact that the cat's paws look like a catcher's mitt. In that vein, naming the cat after famous baseball catchers is an option: Yogi Berra, Johnny Bench, Mickey Cochrane or Mike Piazza are viable names. Snowshoe is another option since the cat's foot resembles one.
Famous author Ernest Hemingway was renowned for having polydactyl cats. In fact, they're sometimes known as Hemingway cats, so naming a polydactyl feline after Hemingway or his famous polydactyl cat Snowball is appropriate. Boy cats can also be named after famous Hemingway characters such as Santiago, Fredric Henry or Jake. Female cats can either be named after his characters, such as Prudie or Renata, or after Hemingway's wives: Elizabeth Hadley Richardson, Pauline Pfieffer, Martha Gellhorn or Mary Welsh.
Polydactyl cats used to accompany fishermen during their journeys, so sea names such as Scurvy, Fisher and Sailor are options. In the end, plays on the word polydactyl also work: Polly, Dack or Countess Poly de Dactyl.