git mv and only change case of directory

You are in a case insensitive environment. Further, adding without the -A will not take care of the remove side of the mv as Git understands it. Warning! Ensure that no other changes or untracked files are around when you do this or they will get committed as part of this change! git stash -u first, do this and then git stash pop after. Continuing: To get around this, do the following:

mv foo foo2
git add -A
git commit -m "renaming"
mv foo2 FOO
git add -A
git commit --amend -m "renamed foo to FOO"

That's the drawn out way of changing the working directory, committing and then collapsing the 2 commits. You can just move the file in the index, but to someone that is new to git, it may not be explicit enough as to what is happening. The shorter version is

git mv foo foo2
git mv foo2 FOO
git commit -m "changed case of dir"

As suggested in one of the comments, you can also do an interactive rebase (git rebase -i HEAD~5 if the wrong case was introduced 5 commits ago) to fix the case there and not have the wrong case appear anywhere in the history at all. You have to be careful if you do this as the commit hashes from then on will be different and others will have to rebase or re-merge their work with that recent past of the branch.

This is related to correcting the name of a file: Is git not case sensitive?

You want to set the option core.ignorecase to false, which will make Git pay attention to case on file systems that don't natively support it. To enable in your repo:

$ git config core.ignorecase false

Then you can rename the file with git mv and it'll work as expected.