When echo %DATE, by default you get dd/mm/yyyy. There is no built in formatting parameter that you can use, so you cannot change the date format unless you rearrange the output characters around.
For example to get yyyy-mm-dd as output, you can do this.
It basically means.
SET Today=%Date:~6,4%-%Date:~3,2%-%Date:~0,2% ^^ ^ ^ ^ || | | | Year| Dash Month Day | Number of chars
Of course the format depends on your local region settings, check %DATE% before you change numbers.