Learn English – How to name something that has sub-categories

I had one of these as a child, and as I recall we just called it a "plastic trumpet".

As this illustrates, not everything has a unique name. In particular, for people outside South Africa those buzzy plastic horns were simply not common or salient enough to warrant a their own non-generic label until very recently. It took a particular event to make most people aware of them as something significant and name-worthy, and when the need for a name arose we simply borrowed vuvuzela from the region where the trumpets had been notable for longer.

You can solve this problem by using different names for each level of the hierarchy. For example, instead of calling it the Service Group, you might call it the Service Division. A Division could be divided into Branches, Branches into Sections, Sections into Groups, and Groups into Teams (or whatever nomenclature you want to use).