AWS Fargate hostname not doable?

This is a known issue in the ecs agent. Have you tried this as a workaround:

echo "$(ip a | grep -A2 eth1 | grep inet | awk '{print $2}' | sed 's#/.*##g' ) $(hostname)" >> /etc/hosts

You can grab the ip and modify /etc/host during the entry point in your container.

I believe there is an ecs agent fix on its way, but I cannot find the issue on GitHub.