The word Amiga is simply a generic name referring to any alternative powerPC computer or OS capable of running a set of programs, which I will recursively refer to as Amiga programs.
It does not refer to the products of any specific company for sometime now, as examples I give, MorphOS, AROS, and Amiga OS 4.
So, now that Amiga, Inc. has let this lapse, it cannot legitimately trademarked by anyone in the United States, as it is a generic term.