When a promotion is renamed, all subsequent promotions of the new name will also promote it with the old name.

To reproduce, I did the following:

1. Create a job test-downstream, leave all settings as-is.
2. Create a job test-upstream, and set the following:
   • Promote builds when ...
     • Name: First promotion
     • When the following downstream projects build successfully: test-downstream
   • Post-build actions, build other projects: test-downstream
3. Save settings, and then click Configure again.
4. Change the name of the promotion from First promotion to Second promotion.
5. Save.
6. Run the build of test-upstream, wait for the build of test-upstream and test-downstream to complete (about 10s with quiet periods etc).

Now you'll observe that the new build has two gold stars: First promotion and Second promotion. Going to /job/test-upstream/1/promotion/ will show First promotion as "Pending promotion" for some reason. It shouldn't be there at all!