To enable a Rename option on the right click context menu for the Inbox, use Regedt32 to edit:
HKEY_CLASSES_ROOT\CLSID\\{00020D75-0000-0000-C000-000000000046\}\ShellFolder
Double click on the Attributes value and change change the REG_DWORD to Hex 50.
If you want a Delete option, change it to Hex 60. If you wish to have both Rename and Delete, change it to Hex 70.
If you delete the inbox and subsequently wish to restore it, edit:
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\Desktop\NameSpace
From the Edit menu, choose Add Key and enter a Key Name of:
\{00020D75-0000-0000-C000-000000000046\}, leaving Class blank. Select this new key and Add Value leaving Value Name blank and set the REG_SZ string to Inbox.
Logoff/Logon.