They probably only paid for Commodore logo
No, they didn't. They had licensed the Commodore logo from Asiarim, who explained in all of its (publicly available) SEC filings that their single licensor CUSA - which was supposed to be their main source of income - hadn't paid yet. Asiarim started to go downhill towards the end of last year, while Barry/Dammy started to hint that CUSA might become the next owner of the trademarks ("Commodore trademark has a new daddy"). Currently, Asiarim and Commodore Holdings - the former owner of the Commodore trademarks - are fighting in court over the ownership of the trademarks.
IMHO, it's pretty safe to assume that CUSA didn't pay any licensing fees for the Commodore logos so far.
but as the Amiga trademark is dead
The "Amiga trademark" isn't dead. The one covering software has been cancelled by the USPTO, but that one was only filed in 2006, IIRC. During the rest of the Amiga's lifetime, there was only one trademark covering hardware - and that one is still alive.
So it could well be that Amiga Inc. have given the name out on a "loan" basis...
CUSA are still many months away from delivering actual Amiga branded product. The recent 'launch' of the Amiga Mini was just a press release and photoshopped pictures.
I'm simply assuming that Barry wouldn't pay
upfront, he can't be
that dumb.
Edit: Just saw on c-a.org that Barry claims the Amiga Mini cases will arrive 'real soon now' (tm), so perhaps payment is due sooner than I thought.