Then maybe I am remembering wrong and what I did was creating a new group with the new name and then deleting the old one. Would that work for you?
1. You do the GET to get the whole definition of your group.
2. You create the new group with the POST and the new name in the XML BODY, using this time "false/false" at the end.
3. You delete the group ID of the original group.
You should end up with the wanted result but it might require some rework on dashboards in case you used the original group as a fixed group.
Maybe GiMMaY would be able to confirm there is no other call to rename a group?