In the build remote API should also show the displayName. It is commonly used to set a version number of the build in for example build pipelines.
Example (https://ci.jenkins-ci.org/view/Jenkins%20core/job/jenkins_main_trunk/3961/api/json)
Current API shows fullDisplayName which includes the projectname and displayname:
"jenkins_main_trunk #3961"
The displayName should show just "#3961".
Makes it easier to for example create external information radiators showing the version/build number for different jobs.