Thanks for posting your question on PI Square. Technically speaking, event frames do not have to have unique names, though if your naming pattern included a time then the name might just happen to be unique. As for structure, let's first consider how elements can be laid out.
Elements are akin to assets or locations and their structure can close resemble your plant hierarchy. The parent-child relationship may be that several assets (elements) belong to a given location (Area in a the plant). For event frames, the most common use of a parent-child relationship is that all the child event frames are sub-events belonging to one big master event. If you set up a multiple trigger analysis to generate event frames, then you will always have 1 parent event frame for the entire event and you may have 0 to many child event frames depending upon which trigger was activated during the course of the overall event.