English derivative of the French forename Henriette or Henrietta, feminine forms of Henry/Henri, from Old German "head of household".
Because Henry and Harold share the common nickname, Harry, Harriet is sometimes adopted as a female form of Harold.
In the 1841 Census of Aberdeenshire there are several spelling variations, the most numerous of which were Hariet, Hariot and Harriot. The 1851 Census for Rathen has rare occurrences of Harriet and Hariot. In general all the variations, including the rare ones Harriett, Hariett, Harriott, Heriot and so on, should be found with a Soundex search.
Whyte gives Eiric as the Gaelic equivalent of Harriet while ONC gives Oighrig.