We are migrating to declarative pipeline and want to invoke another job. This can be done with the build step. Here's how we do it now:

pipeline {
    agent any
    stages {
        ...
        stage('Deploy') {
            steps {
                echo "Deploying ${env.JOB_NAME}..."
                build(job: 'mdh-webapp-deploy-to-dev', parameters: [string(name: 'ARTIFACT_ID', value: '${JOB_NAME}')])
            }
        }
    }
}

The other job is parameterized and takes one parameter named ARTIFACT_ID, in the form of a Choice Parameter.

This is what we see in the log of the pipeline job:

...
Deploying mdh-bestallning-webapp...
[Pipeline] build (Building mdh-webapp-deploy-to-dev)
Scheduling project: mdh-webapp-deploy-to-dev
...
ERROR: Value for choice parameter 'ARTIFACT_ID' is '${JOB_NAME}', but valid choices are [<a list of possible values that includes mdh-bestallning-webapp>]

So it seems that injecting environment variables is not possible. We've tried different syntaxes like $JOB_NAME, ${JOB_NAME} and ${env.JOB_NAME}, but none of them works.

I have had a look at the code, but can't find the correct place to inject environment variables using something like
https://javadoc.jenkins-ci.org/hudson/EnvVars.html#expand-java.lang.String-
If you can point me in the right direction I will try to make a pull request.