Hi Mark, ties in 'kinda nicely' to the New England Putnam family.
The original spelling was de Puttenham. Flemish word meaning putte or well and ham or hamlet, a small village. Or in full a family living near a small village well.
Kinda mates with some of your definitions. AND ... remember the Flemish language came from the German/Dutch border and was used by the Belgiums.
AND also ... The Puttenhams came over from you know where with William the Conqueror. May well be connected, kinda.
But you don't have to call me your cousin Bill. :-)
Bill Putman on the English Putnam line