Name it "My monster", (with the "my").
Think about it.
When you mention it in conversation it sounds awesome ("crap, I gotta feed my monster").
When you call it it sounds awesome ("come here my monster").
When you eat it it sounds awesome ("yeah I'm eating my monster").
When you warn people about it it sounds awesome ("careful, my monster is rather vicious around strangers").
Etc.
DO IT.