When the new version of this board was rolled out the ability to display Parent Stories was removed based on overwhelming feedback from the customer base on the old Kanban. While you cannot display the Parent Stories themselves you can select the parent field for display on the cards.
Another option, if you have the necessary resources, would be to modify the existing Kanban Board code (found here (
https://github.com/RallyApps/app-catalog/tree/master/src/apps/kanban)) to customize it to better fit your needs. I would also recommend visiting Stackoverflow – it is a site where you may get some assistance with this. The following link will take you to the area where developers who use Rally are active:
http://stackoverflow.com/questions/tagged/rally