Shouldn't duplicate group titles be possible?
I suspect the reason is that the requirement that names be unique predates the ability to have parent groups.  That said, allowing non-unique groups would complicate UI design.  For instance, I've seen the scenario where someone has permission to view a parent group but not a child group.  In your case, if someone did that, they'd have no way to differentiate between Customers A and Customers B.

That said, I don't think there's any other compelling reason not to drop the unique index from the name column in civicrm_group and see what happens.  Don't forget to create a new non-unique index once you delete the old one!