You can rename or move a shared folder from the Dropbox desktop app or dropbox.com. In the desktop app, you can rename or move a shared folder like any other folder on your hard drive.
If you rename or move a shared folder, the folder remains shared; however, these changes don't occur in the Dropbox accounts of other shared folder members. Shared folders work this way to avoid confusion among members of your shared folder: nobody wants their folders reorganized or renamed without their knowledge. If you need to rename or move a shared folder for all members, see the following instructions.