Sending cron output to a file with a timestamp in its name
0 0 * * * /some/path/to/a/file.php > $HOME/`date +\%Y\%m\%d\%H\%M\%S`-cron.log 2>&1
Play around with the date format, if you like; just be sure to escape any
\%, as above.
i would highly recommend that you save everything into the same file, using timestamp, as explained here.
and run it thru the timestamping script before saving it to log file (as explained in above link).
You can also append your output to the log file by doing it like this:
0 0 * * * /some/path/to/a/file.php >> $HOME/cron.log 2>&1