If you simply want names then you could use:
git diff --names-only
But if there's no built-in option for this, but it is possible to do this in git, with the help of an "external diff" script.
# run this with:
# GIT_EXTERNAL_DIFF=<name of script> git diff ...
case $# in
1) "unmerged file $@, can't show you line numbers"; exit 1;;
*) echo "I don't know what to do, help"; exit 1;
printf '%s: ' $path
diff $old_file $new_file | grep -v '^[<>-]'
Reference: http://schacon.github.io/git/git.html for GIT_EXTERNAL_DIFF.