It's easy.
You can host a Docker registry yourself (e.g. Harbor or Portus), or use a managed one, like Google Cloud Registry if you use GCP / GKE.
To publish an image to your own registry, you just need to pull from Docker Hub, re-tag the image, and push to your own repo. It's three commands.
You can add some automated and/or manual steps to check the images for security flaws before publishing them.