By default, you can not rename or delete the Inbox icon.
To enable:
Hive: HKEY_CLASSES_ROOT
Key:
CLSID\{00020D75-0000-0000-C000-000000000046}\ShellFolder
Name:
Attributes
Type: REG_DWORD
Value: 72000000 default – can’t rename or delete
Value: 50000000 enable right-click
Rename icon option
Value: 60010020
enable right-click Delete icon option
Value: 70010020 enable right-click Rename or Delete icon
option
If you want to delete the Inbox icon, its safer to use TweakUI.