"to insist on payment of debt," 1620s, perhaps related to dunnen "to sound, resound, make a din" (c.1200, dialectal variant of din), or shortened from dunkirk (c.1600) "privateer," a private vessel licensed to attack enemy ships during wartime, from Dunkirk, French port from which they sailed. The oldest theory traces it to a Joe Dun, supposedly a London bailiff famous for catching defaulters. Related: Dunned; dunning. As a noun from 1620s.
Old English dunn "dingy brown, dark-colored," perhaps from Celtic (cf. Old Irish donn "dark;" Gaelic donn "brown, dark;" Welsh dwnn "brownish"), from PIE *donnos, *dusnos "dark."