What is the name of Amazon's managed Kubernetes service?

Amazon's managed Kubernetes service is Amazon Elastic Kubernetes Service, commonly abbreviated Amazon EKS. It lets organizations run Kubernetes clusters on AWS while Amazon manages much of the control-plane infrastructure.

Kubernetes is an open-source system for deploying, scaling, and managing containerized applications. EKS connects that orchestration layer with AWS services such as networking, identity, storage, monitoring, and compute. Organizations can run worker capacity on Amazon EC2, use AWS Fargate for serverless pods, or combine other supported compute options.

The alternatives describe different AWS products. Amazon ECS is a separate container-orchestration service that is not Kubernetes. Amazon ECR is a container-image registry, while Fargate is a serverless compute technology that can run workloads with EKS or ECS. EKS therefore is the precise answer to the question.