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1. English: topographic name for someone who lived by an ash tree, a variant of Ash by misdivision of Middle English atten ash ‘at the ash’, or a habitational name from any of the many places in England and Wales named Nash, from this phrase, as for example Nash in Buckinghamshire, Herefordshire, or Shropshire. The name was established from an early date in Wales and Ireland.
2. Jewish: of unknown origin, possibly an Americanized form of one or more like-sounding Jewish surnames.

(Dictionary of American Family Names, Oxford University Press)

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