Exactly. And this was the major cause of trouble between Apple Computer and Apple Corps, because they had an agreement that Apple Computer would never distribute music.. so when iTunes was made, Apple Corps (understandably) took umbrage. Equally the record label "Amiga" (it's a German record label) never had a problem from Commodore or Amiga Inc as the two were in separate markets.
But then you knew that already, I'm sure. 
Having two platforms with the same name "Amiga" would never be allowed, though.
Indeed, but not being a trademark attorney I do have a question about another aspect....use.
Example:Amiga Inc. ended up using AmigaOne. Let's dismiss the notion that constitutes "use" of the trademark, since court has since decided AmigaOne is not Amiga.
The Amiga license to IContain was revoked and product cleared out on Alibaba. The Amiga license to CommodoreUSA for the Mini resulted also in product which never really saw an actual distribution.
That one is still funny since Amiga Games Inc. who are simply NOT Amiga Inc. claim the mini as part of their history.
"Use" is a factor in holding on to trademark, from my basic readings anyway.
If you discount the above, can you post a list of Amiga branded products here during the entire time of trademark registration by Amiga Inc.? I'm curious...
#6