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I used to believe that the name Knapman was associated with flint knapping (the making of arrow and spear points, and subsequently the supply of strikers for flintlock firearms and the production of building materials). Knapping was an important activity in places such as Brandon in Suffolk, and some parts of Norfolk and Sussex. However, the 1841 census shows that almost 88% of the 471 Knapmans (or close variants of the name) in Great Britain at that time were living in Devon, while there were no Knapmans in Suffolk or Sussex, and just one family group in Norfolk, who had brought the name from Devon. At that time there were also 112 persons called Knapper in Britain, 91 of them in Staffordshire; 1,051 called Knapp (over half of them in Middlesex, Berkshire, Gloucestershire, Wiltshire and Hampshire); and 564 called Napper (two thirds of them in Sussex, Somerset and Middlesex). If anyone took their name from knapping, these seem to me to be stronger candidates.
If the name does not come from flint knapping, the most likely derivation seems to be the term knap which is widely used in Devon to signify a hill, or the crest of a hill, and which has its origins in the Old English word cnæpp meaning top, and possibly the Old Norse word knappr meaning knob. This conclusion is endorsed by ‘Patronymica Britannica’ , which describes Knapman as meaning “a dweller upon a knap or hill”. However, this begs the question of why the name is not more widely distributed.