You can easily get a date in any format, although I would use an ISO8601 format, which has the advantage of being unambiguous and sortable e.g.
date "+%Y%m%dT%H%M%S"
gives
20131116T122633
You can use this in a script to construct your file name, using any other charactescharacters to construct the name.
echo Test > File`date "+%Y%m%dT%H%M%S"`.txt