Question , can MinIO the company assert AGPL copyright against the fork - i see in the writeup they mentioned trademarks as far as the fork is concerned.

Whats the situation for a AGPL fork , were one to use it can the company assert rights like they did to Nutanix.

As long as the fork complies with the terms of the AGPL, Minio can't stop them from using the code. As the article acknowledge,s hey could potentially rely on trademarks to make them rename it.