The log file already contains date information on the files, but if you want the date/time as part of the filename, you can do something like:
Code:
rsync -a src dst --log-file="rsync.log.$(date +%Y%m%d%H%m%S)"
The $() expression will run the date command (with format YYYYYYMMDDhhmmss) to include as part of the filename.