You can set a variable with the result of running the date command, and then use that as a filename, if that's what you want, like this:
Code:
myfilename="fileame_with_date_$(date +%Y%m%d)_in_the_middle"
echo "This will end up in my file" > "$myfilename"
The +%Y%m%d argument to the date command tells it to return the results in YYYYMMDD format, which is my preference for a well formatted date (it's a very good format because lexical sort order is the same as chronological sort order!).