As far as I can tell, you need to modify the function git-vc-print-log. It only has some limited configurability, and that's not enough for you. You can change the variable vc-git-root-log-format to change what vc-print-log displays for a directory, but that only gives you a value that's passed to git log --pretty=tformat=, and there's no option to include the list of file names there. You need to add the option --name-only or --name-status as a separate argument to git.
You need to change the way git-vc-print-log calls vc-git-command. While it would technically be possible to do it with advice, it's a bit tricky. Given that the function is fairly small and only really does one thing, I'd just write my own modified version. Take the existing code and pass the extra option.