A Search Box scope group’s settings include its ID, name, description. Once a group is created, you can no longer change its ID, but you can edit its name and description at any site level as follows:
1. Go to the Search Box Scopes page for the site level at which you want to create the new scope group as described in “Search Box Settings and Inheritance”.
2. Click on the target group name and select Edit Group or Overwrite Inherited Group from the action menu.
3. You should now be on the Edit Search Box Scope Group page.
Make the following settings:
Name: Enter a name for the group as it should be presented on the Search Scopes page at the current level and below.
Description: Enter a short description for the group. This will help remind yourself and other administrators about the intended purpose of the group.
4. Click on OK to close the Edit Search Box Scope Group page and store your settings.
Note that if you edit the name and/or description of an inherited scope group, then your settings will apply at the current site level (and below) only. Furthermore, these settings will no longer track changes made at higher levels in the SharePoint hierarchy.