I know what you mean: I regret having the name of a human being, and tried to be a bandicoot for a post or two but it didn't catch on, and I fear I am doomed to remain a furry animal trapped in a woman's body <sigh>
Common animals that start with the letter M include the Macaque, Macaroni Penguin, Muskat, Madagascar Hissing Cockroach, Magellanic Penguin, Magpie, Mallard, Manatee, Mandarin Rat Snake, Mandrill, Marine Iguana, and Meerkat.
There's also mouse and marsh frog
Magpie is obvs taken, Meerkats are too common [not in the snobby sense], mice are too like gerbils...
I see AI having a lot of fun with Macaroni Penguin, though I think that actually belongs under 'P' not 'M'.
I'd like to see what AI would make of 'Madagascar Hissing Cockroach' , but I'm not sure I'd want one around the Bluestocking.. the hissing would disturb the gerbils' 70s tribute band performances.
Mallard - well you'd have to be blue, streamlined, and capable of reaching 126mph..
So I'd go for MyrtleMountainLion...