I am part of the project. If your last name was spelled originally Claxon, Claxson or Clackson, as mine was, the origin is Danish. Probably from King Harold KLak and Harold Klackson, whose sons, Harold Bluetooth and Svein Forkbeard, who invaded East Anglia and Essex in @920. Clacton on Sea was The Village of Clacks Sons in early days.
The name means Stone Cutter/ Hatchling depending on origin.
A very ancient name, whether Saxon or Dane. ( Saxon is Clac).
Klak is probably the sound an implement makes when carving on stone.
Rich