I've come late to the thread, but this jogged my memory about what HAM said about the choice of Archewell for their foundation and thus their firstborn's name Archie, its roots in an ancient Greek concept of profound wells of giving or some such. Gemini has set me straight on the subject
The name Archewell is built on the ancient Greek word Arch\bar (\alpha\rho\chi\acute{\eta).
In ancient Greek philosophy—pioneered by Pre-Socratic thinkers like Thales, Anaximander, and Heraclitus—Arch\bar represents the "first principle," "origin," or "source of action". It refers to the fundamental substance or ultimate cause from which everything originates and by which all else is governed.
The Duke and Duchess of Sussex explained that this concept inspired both the name of their foundation and the name of their son, Archie Harrison Mountbatten-Windsor. They combined the Greek concept of arch\bar (meaning a "source of action") with the English word well ("a plentiful source or supply") to signify a "deep reservoir to draw upon."
Unfortunately Archewell seems to have petered out, as has any sort of coherent principle or "source of action" at all, evidently. I personally associate "Archie" with Archie Rice in John Osborne's The Entertainer, clearly considered by the playwright to be an appropriate name for a clapped out, somewhat desperate middle-aged guy with broken dreams hawking himself about the place.