A room is a model element. You can add a room to a design option. A room tag, however, is a view-specific annotation element. When you tag a room that is part of a design option, the room tag is part of the view, not part of the design option.
By default Revit displays room tags for rooms that you add to a design option. If you later create a dedicated view for that design option, room tags display if you create the view using View tabCreate panelDuplicate View drop-down (Duplicate with Detailing).