I know this is an older post, but someone will stumble across it in a Google search and it also looks like some questions the OP asked in comments weren't specifically addressed. Also, please go easy on me since this is my first answer posted on SO. :)
To redirect the output to a file using a dynamically generated file name, my go-to (read: quick & dirty) approach is the second solution offered by @dbenham. So for example, this:
@echo off
> filename_prefix-%DATE:~-4%-%DATE:~4,2%-%DATE:~7,2%_%time:~0,2%%time:~3,2%%time:~6,2%.log (
echo Your Name Here
echo Beginning Date/Time: %DATE:~-4%-%DATE:~4,2%-%DATE:~7,2%_%time:~0,2%%time:~3,2%%time:~6,2%.log
REM do some stuff here
echo Your Name Here
echo Ending Date/Time: %DATE:~-4%-%DATE:~4,2%-%DATE:~7,2%_%time:~0,2%%time:~3,2%%time:~6,2%.log
)
Will create a file like what you see in this screenshot of the file in the target directory
That will contain this output:
Your Name Here
Beginning Date/Time: 2016-09-16_141048.log
Your Name Here
Ending Date/Time: 2016-09-16_141048.log
Also keep in mind that this solution is locale-dependent, so be careful how/when you use it.