Bernhard’s answer needed some tweaking work for me because the %DATE% environment variable is in a different format (as commented elsewhere). Also, there was a tilde (~) missing.
Instead of:
set backupFilename=%DATE:~6,4%%DATE:~3,2%%DATE:0,2%
I had to use:
set backupFilename=%DATE:~10,4%%DATE:~4,2%%DATE:~7,2%
for the date format:
c:\Scripts>echo %DATE%
Thu 05/14/2009