Alice's pet cat in Alice's Adventures in Wonderland is Dinah. Alice thinks about Dinah soon after falling down the rabbit hole and later talks about her while meeting the Mouse and other animals near the pool of tears.
Dinah is more than a passing reference: Alice describes her as a skilled catcher of mice and imagines how useful she would be in Wonderland. Mentioning a cat makes the nervous animals uncomfortable, helping drive the comic confusion of the Caucus Race scene. Dinah remains part of Alice's remembered home life while Wonderland becomes increasingly strange.
Readers sometimes confuse Dinah with the Cheshire Cat, but they are different characters. The Cheshire Cat is a grinning Wonderland creature who can disappear, whereas Dinah is Alice's ordinary household pet. Dinah is also mentioned in Through the Looking-Glass, reinforcing her role as Alice's familiar companion rather than a Wonderland resident.