Oh urrr... I admit my first thought was maybe her parents had a sense of humour and went with Brie (sometimes spelt Bree when a name)? XD
Possibly One starting with M like Milly, Maisy or Molly so it flows with mouse? Or if you wanted a different letter (and different to your other chars names) maybe Jean, Paige, or Chloe?
Any of those sound right to you? No worries if another one you prefer comes to mind too. Shall be sure to let you know if any more come to mind.
Oh urrr... I admit my first thought was maybe her parents had a sense of humour and went with Brie (