When Prince Harry and Meghan Markle welcomed their first child, Archie Harrison Mountbatten-Windsor, in May 2019, they decided not to give him a royal title. Mountbatten-Windsor is the official last name used for members of the royal family who do not have the "royal highness" styling.
And since stepping away as senior members of the royal family, Markle and Harry have opted to give their son an even more normal upbringing in the United States. In the wake of Queen Elizabeth II's death, though, Archie is now considered a prince as the grandchild of King Charles III.
Per the rules of peerage, which dictate British royal titles, Archie officially became a prince when his grandfather Charles acceded to king on Sept. 8. The current rules, issued by King George V in 1917, state that the title of prince or princess goes to the sons and daughters of the sovereign, grandchildren born to the sovereign's sons, and the eldest son of the Prince of Wales's eldest son (who would be Prince George today). This is why Prince Andrew's children, Princess Beatrice and Princess Eugenie, are princesses, while Princess Anne's children, Peter and Zara Phillips, are not. The queen reportedly offered a "courtesy" title to Zara and Peter, but Princess Anne apparently declined.
The Queen did make a change in 2012, decreeing that all children born to the eldest son of the Prince of Wales (aka Prince William) would have the title prince or princess upon birth. Thus, we have Princess Charlotte and Prince Louis. Assuming no more changes to the rules are made, Archie is a prince — per the aforementioned 1917 rule. Archie could also inherit the Duke of Sussex and other titles from Harry one day. Archie is already entitled to use one of Harry's "lesser" titles, like the Earl of Dumbarton, but it appears they have decided not to.
Of course, Archie can still decline to use the prince title — but we think Prince Archie has a nice ring to it.