The best way to do this is by running the command:
git diff --name-only --cached
When you check the manual you will likely find the following:
--name-only
Show only names of changed files.
And on the example part of the manual:
git diff --cached
Changes between the index and your current HEAD.
Combined together you get the changes between the index and your current HEAD and Show only names of changed files.
Update: --staged is also available as an alias for --cached above in more recent git versions.