Although documentation is clear that this is not supported, there is a workaround. You can create a bootstrap_ecs.sh file and override the container ENTRYPOINT to reference this at runtime (or else add the below to your own bootstrap script). You can use this when running from ECS. Otherwise, use your standard ENTRYPOINT and COMMAND.

bootstrap_ecs.sh

#!/bin/bash

ifconfig # prints full IP info
echo "Detecting 'eth1' interface..."
DETECTED_IP=$(ifconfig -a | grep -A2 eth1 | grep inet | awk '{print $2}' | sed 's#/.*##g' | grep "\.")
if [[ -z $DETECTED_IP ]]; then
    echo "Detecting 'eth0' interface ('eth1' not found)..."
    DETECTED_IP=$(ifconfig -a | grep -A2 eth0 | grep inet | awk '{print $2}' | sed 's#/.*##g' | grep "\." | head -1)
fi
DETECTED_HOSTNAME=$(hostname)
echo -e "\n\nDETECTED_IP=$DETECTED_IP\nDETECTED_HOSTNAME=$DETECTED_HOSTNAME\n\n"
# Note: newer OS versions us `ip` instead of `ifconfig`

# Echo for debugging. You can comment/delete the 1st and 3rd lines once everything is working.
echo -e "Current file contents:\n $(cat /etc/hosts)"
echo "$DETECTED_IP $DETECTED_HOSTNAME" >> /etc/hosts
echo -e "\n\n\nUpdated file contents:\n $(cat /etc/hosts)"

CMD="$@"
$CMD

AWS documentation says The hostname parameter is not supported if using the awsvpc networkMode. Anything but awsvpc is not supported with FARGATE, therefore there is no way to set hostname in task definition with FARGATE launch type.

Let me share a tip that I have applied for setting up the Avro Schema Registry. It could be helpful in answering this question. Schema Registry requires setting the SCHEMA_REGISTRY_HOST_NAME environment variable. With AWS Fargate and awsvpc networking mode there is no way to explicitly set the host name property inside the task definition, as was already pointed out in this thread. For horizontal scaling you need multiple registry instances each having its own SCHEMA_REGISTRY_HOST_NAME value. I had overridden the Command property in a task definition in the following manner (the HOSTNAME is provided by Docker and under awsvpc regime it reliably reflects the host name):

sh,-c,export SCHEMA_REGISTRY_HOST_NAME=$HOSTNAME;/etc/confluent/docker/run

The downside of this approach is that you now depend on the implementation detail of the image; in this case the original CMD statement from the Dockerfile. This is why it is always important to use a specific version tag with an image name instead of relying on the latest tag.

P.S. As a reference, here is my original comment on Issues 1126 for Schema Registry.