The Barebone family was a historical No-Maj American family descended from Scourers and known for being anti-magic. At least one adopted member was found to be magical, however (WFT).
"Barebone" hints at the Puritan Sourer legacy Bartholomew and his family carry on; first, it alludes to the austerity of Puritan sensibilities; second, Praise-God Barebone was an English Puritan of the Commonwealth/Interregnum (the period of English history between the English Civil War and the Restoration of the monarchy, when Puritans basically controlled the government and instituted reforms related to their religious and moral beliefs) who belonged to a sect particularly concerned with Judgement Day and whose name is used in reference to the appointed parliament which immediately preceded Oliver Cromwell being made Lord Protector (Barebone's parliament). (Sources: Wikipedia 1, 2, 3, 4, 5)
The names Chastity, Modesty, and Credence are reminiscent on Puritan naming conventions (Source: Slate).