This issue seems to have been dropped from here:
https://code.google.com/p/build-pipeline-plugin/issues/detail?id=135

Text is from that issue, repeated here:
What steps will reproduce the problem?
1. Create a project with a name like "build_version_1"
2. Under Advanced Project Options set a custom display name like "Build V1"
3. Set up a build pipeline view with that project included

What is the expected output? What do you see instead?

I expect the projects in the pipeline to use the display name. Instead they use the name. If display name is not manually set, it returns the same value as name. So, display name should generally be used.

What version of the product are you using? On what operating system?

Jenkins: 1.484
Build Pipeline Plugin: 1.3.3
OS: Windows (various versions)

Also, as noted by a user on the original issue :

This is useful when you have 2 projects my-project-deploy-pre-prod and my-project-deploy-prod, and in pipeline view all you see is prefix. You may deploy in prod box by mistake. It is not clear what you are launching at the moment.