AFAIR, the operating system as a whole, originally did NOT have a single name but as you said consisted of basically three names:
Kickstart (what we would call BIOS today)
AmigaDOS (the CLI -later shell- part)
Workbench (the GUI)
...you could find use of other names (which are in fact OS parts though, but their version generally does describe the whole system version) like kernel, exec or intuition.
After 3.0 I'd say (but could be 2.04 - definitely before ESCOM though), there were the first mentions of AmigaOS, describing the whole thing as an entity.
I prefer not having a single name.
So there is a triad that rules everything... kickstart/amigados/workbench