The cat in the story "Alice in Wonderland" goes by the name of Cheshire Cat. Certain variations include the Cheshire Cat and Chessur, or Chess for short, as used in the 2010 movie adaptation of the book.
Even though the Cheshire Cat was made famous through the work of Lewis Carroll and the many movie adaptations that followed, the saying "grinning like a Cheshire cat" was a proverbial saying already being used. The saying is thought to come from Cheshire cheese molds, which were designed as a smiling cat. The Cheshire Cat is a male Tabby from the Lavette Family.