In this curious case I'm facing here, I'm unable to change any item's Display Name.
I have tried changing DisplayName from Ribbon menu, from Appearance section and Sitecore Rocks. I can write new text but after save when item is reloaded it is still old Text in DisplayName. I have tried cache clearing as well.
I have tried lot different of ways to track down if the issue is with Sitecore setup, or My code (like may be events handlers, pipelines, etc), or may be database.
Finally found that issue is with database when i tried this database with clean Sitecore instance pointing it. And I was able reproduce the editing not working anymore in clean Sitecore instance.
Next I'm not sure how to identify what is the issue in this database that I'm unable to edit Display Name only. Rest of the fields I'm able to edit.
Note: Sitecore 7.5 update-2