The Official Title Of Their Son
Prince Harry and Meghan Markle chose to reject any royal titles for their son. At the very least, this is the case while he is young. Archie could have become the Earl of Dumbarton, which is a title that is held by his father in Scotland. However, they insisted that he will just be called “Master Archie” for now.
They Will All Move Up The Succession
These things might change upon the eventual death of the Queen. Once that happens, everyone in the line of succession will move up. Charles is going to be the king, and Prince William will turn into the direct heir. As the grandchild of the reigning monarch, Archie is entitled to the “Prince” title if he wants it.