In the words of her sister, Shirley (Provided at Mouse's 80^th birthday):

She didn't look like a mouse. She didn't act like a mouse. She had never expressed any great interest in cheese, and had never been caught in a trap. She had a good rapport with most cats. However …

She did have a small sister whose mission in life at that point was to assign more suitable names to certain favored members of the household. Already there was "Snucky", a brother who later graduated to the more dignified "Peter Rabbit"; her mother, known as "Puss", and her grandmother "Hoppy", who had some mysterious connection to Hopalong Cassidy. And since mice were her favorite kind of people, what better name for a deserving sister than "Mouse"?

There was no formal christening, but "Mouse" became accepted as the preferred appellation, sometimes appropriately modified by "Aunt" when used by small children.

After some years of successful mousehood, ever increasing activities eventually made "Mouse" seem inadequate. In an inspired moment she was re-named "Mice", which seems to more aptly cover the wide range of her every-day adventures. So that's why.

* Mice is also an abbreviation for MI-CESTER