git diff --name-only "@{3 days ago}" "@{2 days ago}"

changelog.txt
newfile.txt

git diff --name-status "@{3 days ago}" "@{2 days ago}"

M       changelog.txt
A       newfile.txt

git log --since="1 day ago" --name-only --pretty=format: | sort | uniq

git whatchanged --since '04/14/2013' --until '05/22/2014' --oneline --name-only --pretty=format: | sort | uniq >> changedlist.txt

$ git --version
git version 1.7.8.rc0.35.gee6df
$ git whatchanged --since '10/27/2011' --until '10/30/2011' --oneline
55e7c0a (squash) test for previous
:100755 100755 dbf623b... 53905a2... M  t/t8006-blame-textconv.sh
2564aa4 blame.c: Properly initialize strbuf after calling, textconv_object()
:100644 100644 173f286... e39d986... M  builtin/blame.c
e8e1c29 Update draft release notes to 1.7.8
:100644 100644 3045245... ddb8d37... M  Documentation/RelNotes/1.7.8.txt
8debf69 clone: Quote user supplied path in a single quote pair
:100644 100644 488f48e... efe8b6c... M  builtin/clone.c

git log --after="2015-11-05T16:36:00-02:00" --before="2015-11-15T16:36:00-02:00" --pretty=format:"" --name-only | sed '/^s*$/d' | sort | uniq -u