Genuine question: why Amazon EKS and not Amazon Kubernetes then? I noticed every single managed Kubernetes doesn't call it Kubernetes.

Huh?

EKS => Amazon Elastic Kubernetes Service

Kubernetes is a little different here... it seems a bit more nebulous from an installation/instance point of view. It's a bit like saying we use "Linux". Which Linux? Debian? Ubuntu? RHEL? SUSE?

Because that Trademark is owned by the Linux Foundation who are very well positioned and financed (AWS themselves are Platinum members) and published clear usage instructions.

As someone else said, what constitutes "Kubernetes" isn't well defined, and so the CNCF put limits on using the terminology in product names.