This happens when your opponent starts relocating their HQ. While the relocation is underway, the HQ icon will appear in the city where the HQ is currently situated, and the HQ where the relocation will take place. It is only once the relocation is complete that the opponent will be down to 1 HQ icon again!

Please note that the visual of two capitals does not provide your opponent with any additional benefits or advantages. This is purely visual!