Statistics notwithstanding, the term diminutive is not restricted to names. It can be used with any noun as in kitty, doggy, superette (small supermarket), etc.
FYI, Polish is one of ther few languages that has an augmentative form. As oposed to the diminutive which makes thigns sound smaller, cuter, daintier than the original, the augmentative makes things sound bigger, older, coarser or possibly more threatening.
Pies (dog), piesek (cute little doggy), psisko (big, old, clumsy cur).