Multiday items will (by design - like in Outlook) be displayed in the header for each day where the event occurs.

You can do this by setting the property PlannerItem.InHeader :=true.
This means that for a non databound planner, you should add an inheader item for each day where the event occurs. In the TPlanner this can't happen automatically as there is no imposed fixed relationship between positions (columns) and days or resources you use.
Please make sure to increase Planner.header.Height so items can be shown there.

For the DB-aware TDBPlanner, this is handled automatically. TDBPlanner will display the items that span multiple days in the header for each day where the item occurs. It will display this as an item in the header on each day. It can indicate in the caption (when you set PlannerItem.CaptionType = ctTime) the start/end time of the item.