The yyyy-mm-dd format (ISO 8601) is the only one that is unambiguous, because no one so far in history has ever used the yyyy-dd-mm format (at least until some xkcd-reading jokester probably will start using it just out of spite). I use ISO 8601 everywhere. It has the additional benefit that filenames get sorted correctly in lexographical order.
Because 'International Organization for Standardization' would have different acronyms in different languages (IOS in English, OIN in French), our founders decided to give it the short form ISO. ISO is derived from the Greek word isos (ίσος, meaning "equal"). Whatever the country, whatever the language, the short form of our name is always ISO.