Okay, I may have you both beat! Our Cockateil's name is "Birdy-Bird"! I named him Oglethorpe, and my husband hated that. He called him Birdy-Bird while we were thinking of other names, needless to say, it stuck.....10 years later, he is still Birdy-Bird.
I once saw a little guy like this in a store, and I said if I got him, I'd name him Squirrel. His coat was exactly like that of a squirrel. This one looks the same. I think you should name it that.