They don't own the trademarks, there's a lot of interesting history [1] and it seems a company called Polabe Holding [2] does. The allegation seems to be that they acquired Commodore USA assets which included a license to use the trademarks [3], but the company they were licensed from did not actually own the trademarks [4] and lost a lawsuit over it.

I think this only scratches the surface, it seems like a delightful mess. It doesn't look like they have any rights to use the trademark, though.

1. https://www.nostalgianerd.com/commodore-heist/

2. Either purchased from or f/k/a C= Holdings. https://trademarks.justia.com/owners/polabe-holding-n-v-4321...

3. https://www.prlog.org/10884490-commodore-announces-exclusive...

4. https://www.sec.gov/Archives/edgar/data/1415813/000101968714...