Prince Harry surname is Mountbatten-Windsor whereas Meghan is no longer a Markle, she publicly called as Meghan The Duchess of Sussex for her Archewell Audio podcast with Spotify and his son name Archie Harrison Mountbatten-Windsor.
Much like sister-in-law Kate Middleton, Meghan is still widely known by her maiden name in some circles.
While neither Harry nor Meghan have been using His/Her Royal Highness since they resigned as senior working members of the British royal family in January 2020, they are still The Duke and Duchess of Sussex when it comes to life outside the royal family.