The headline says "The meaning behind the royal baby's name". I hope it has meaning, as it seems a strange and unusual choice. The bookmakers had Alexander, Arthur and Albert. Who would guess that the name Archie is in the top 50 names since 2003. CNN claims that instead of a traditional royal name, they chose a name they loved. So there aren't really any Archies or Harrisons among the names of any British monarchs or their immediate offspring.
So it turns out there is no meaning behind the name. The Royal family succession tree is shown in the articles with its colour coding for royal bloodline, in line to the throne, married and divorced. Archie is seventh in line to the throne, so does not quality immediately for the title of prince. He has the right to use his father's second peerage title, Earl of Dumbarton. When Prince Charles becomes King, Prince Harry's son will automatically become His Royal Highness Prince Archie Harrison Mountbatten-Windsor.
Rules abound with the royal family - they have had centuries to make rules. Here's the note on the Queen's purse and its social signals:
"The Queen isn't one to be rude, and so her purse is used to send subtle social signals. When she places her clutch on the table at dinner, it means it's time to wrap things up–so consider the bite you're reaching for your last. When she swaps her purse from her left hand to her right, it means she'd like to finish up her conversation."
This little Fritilleria is blooming in the garden now. What a strange and amazing checkerboard flower - I gave it an ornate background to match its mood.