Her name was "Mimsie"

YouTube link.

In the standard version of the logo, as first used on The Mary Tyler Moore Show, Mimsie appears in a crouched position, looks up at the camera, and meows once. Mimsie would not meow for the camera crew, so they eventually used footage of her yawning, run in reverse, with the sound effect added. By the 1980s, there were many different variants of the logo, with Mimsie often appearing in different painted “costumes” corresponding to the style and theme of the particular programs. For the detective series Remington Steele, a Sherlock Holmes-esque stalking cap and pipe were added; The White Shadow featured a basketball with Mimsie; Hill Street Blues painted a police uniform hat onto Mimsie’s head; St. Elsewhere used a surgical mask; in contrast, Newhart kept the original, unadorned footage, but replaced the sound effect with Bob Newhart’s voice-over of “meow” in his trademark deadpan style.