Strictly speaking, 'Van Schouw' is not a surname. The term, 'the Van Schouw family group' refers to descendants of Claes Cornelissen van Schouw, and includes present-day male-line descendants of the surnames Garrabrant, Clawson, Peterson and some variants. Claes Cornelissen immigrated to New Netherland prior to 1640. No known record dispositively identifies Claes Cornelissen's place of birth or his parents. In New Netherland, he and his children used patronymic naming according to Dutch tradition, i.e., they used 'Claes' or 'Claesen' as their second names. His grandchildren by his son Willem adopted the surname Clawson. His son Gerbrant's children used the second name Gerbrantsen; variants of that name were used by all of Gerbrant's grandchildren, except the descendants of Gerbrant's son Pieter, who adopted the surname Peterson. 

The Van Schouw surname project at Family Tree DNA was established about 2006 by Clawson descendant Frank Crosswhite (d 2008), mainly to verify the existence of living members of all three lines via Y-DNA. That goal has been accomplished. In addition, Y-DNA results demonstrate the existence of unrelated Clawson and Peterson lines.