We recommend to set DD_TAGS to identify your different environments.
To get some further information from the applications we provide an example for jmx. It is configured mainly in <SMARTIDHOME>/docker/compose/tools/datadog/conf.d/jmx.d/conf.yaml
It's configured to connect to idm-operator:5000 without ssl. This port isn't listening by default, to enable it check <SMARTIDHOME>/docker/compose/identitymanager/operator/docker-compose.yml.
You can also setup ssl and authentication for this. As long as you know what containers you have running and don't adding a port mapping there shouldn't be an security issue by using it this way.
To provide an example of how to add additional attributes which are available as MBeans there is tomcat.connections.count and tomcat.thread.count.