Solved! Go to Solution.
You can rename a folder in the Browse Files view. Click on the folder you want to rename, and a "Folder Actions" column will appear on the far right. One of the listed options is to "Rename Folder".
Very silly that you cannot move reports between folders...
Elliott Lowe, I believe you can cut reports from one folder and move to another.
On the right hand panel, you can either cut or copy a report, then navigate to the folder you want to move it to, and click "paste". Here are a couple screen shots: