This seems to be the only way to set ENVs with dynamic values in beanstalk. I came up with a workaround that works for my multi-docker setup:
1) Add this to your Dockerfile before building + uploading to your ECS
    repository:
CMD eval `cat /tmp/envs/env_file$`; <base image CMD goes here>;
2) In your Dockerrun.aws.json file create a volume:
{
    "name": "env-file",
    "host": {
        "sourcePath": "/var/app/current/envs"
    }
}
3) Mount volume to your container
{
  "sourceVolume": "env-file",
  "containerPath": "/tmp/envs",
  "readOnly": true
}
4) In your .ebextensions/options.config file add a container_commands
    block like so:
container_commands:
  01_create_mount:
    command: "mkdir -p envs/"
  02_create_env_file:
    command: { "Fn::Join" : [ "", [ 'echo "', "export ENVIRONMENT_NAME=" , { "Ref", "RESOURCE" }, ';" > envs/env_file;' ] ] }
5) eb deploy and your ENVS should be available in your docker container
You can add more ENVs by adding more container_commands like:
  02_create_env_file_2:
    command: { "Fn::Join" : [ "", [ 'echo "', "export ENVIRONMENT_NAME_2=" , { "Ref", "RESOURCE2" }, ';" >> envs/env_file;' \] \] }
Hope this helps!