The `YYYY-MM-DD` format is the best option for most use cases. Reasons the alternatives are worse:
1. `YY-MM-DD` is too ambiguous. `DD-MM-YY` is much more common, so, e.g. if you write 21-06-16 in `YY-MM-DD`, most people will parse that in `DD-MM-YY`, i.e. 21st June 2016, not 16th June 2021.
2. `DD-MM-YY` doesn’t work for Americans. If you write `02-01-2015`, an American will see 2nd February 2015, while most of the rest of the world will see 2nd January 2015.
3. A human-friendly format like `16th June 2021` is easier to read (assuming your audience speaks English), but if you sort alphabetically, you won't get a list of files from new to old.
Thankfully, nobody uses `YYYY-DD-MM`. This means that basically everyone reads `YYYY-MM-DD` correctly, even if it is a bit unfamiliar.
If you know you won't need to sort, use a human-friendly format. Otherwise, go for `YYYY-MM-DD`.