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.
The rename or move isn't reflected 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 a shared folder for all members, see the following instructions.