Mozzarella because it sounds kinda like Cinderella, in whose Disney animated film had mice sing about her.
Swiss had to be white and full of holes in some way, so he's covered in scars, has a chip on one ear, and owns a Swiss Army Knife because mice using human tools is so adorable.
American themed more around her color scheme and me wanting to draw some stars. American cheese is usually either white or dyed yellow/orange, but we love our artificial blues so why not?
Submission will be updated as I make more mouse characters themed after cheeses or get more art of these characters.