Not a mechanic, but I have named my old BMW (though none of my other current cars - I did name my old BMW station wagon "Uber Wagon" back when the "Swagger Wagon" commercial was on TV). In other words, I'm the kind of person who would name things.
It wouldn't occur to me to name a tool chest or cart. I suppose if it were a color it could pick up a name ("Big Red", the Pumpkin, or something like that), but I kinda doubt it.
I'm not a giant fan of stickers either - not sure why. My box and cart are both fairly new, but I don't think many stickers will make their way on either. Maybe a few on the cart...