Amiga Inc own the rights to the name Amiga Inc. They can keep going as this. Also, they own the rights to the Amiga name in europe (what BBRV is trying to get will only apply to the US IIRC).
Also, Hyperion own the rights to the name AmigaOS, which means that's safe aswell.
If anyone bought the name Amiga (the one that's been abandoned in the US) they will be able to produce software and call it Amiga whatever.
Amiga Inc, AmigaOS and AmigaOne are all safe. Well, they are in Europe nyway ;-)