There's also Ulysses S. Grant. The "S" was apparently just a mistake on his enrollment at West Point. His birth name was Hiram Ulysses Grant. He tried to switch his first and middle names, but ended up with the initials USG instead of UHG.
And then there's the odd case of "Thomas a Becket." Thomas Beket was never called Thomas a Becket in his lifetime. He apparently went by many names, one of which was "Beket," but never "a Becket."
In Wales they used to use ab/ap as a patronym, a bit like Mac in Gallic.
There might have been similar in parts of whatever they called England before the anglo-saxons came, but that's not likely to have influenced anything by the time of Becket, or the later time when the 'a' was added.
I don't think it has really survived in Wales either; the 'a' has often dissapeared and the p/b merged with the fathers name, like Prichard, or Bowen.
There is a theory that America is named not after Amerigo Vespucci, but after Richard ap Meryk also known as Richard Amerike, who owned the ship that sent John Cabot across the Atlantic. I think it's mostly been refuted at this point, but the name has stuck with me.