The first name Kaj is female and male.
The origin of the name Kaj as a form of Kai is not clear. It is presumably a Frisian short form of Gerard or Nikolaus, but as well of the Latin name Cajetanus and is of Celtic origin. It is a name for boys and seldom for girls (from Latin Cajetana or Katharina).
Kaj means “warrior” (from Frisian “kempe”), “victory of the people” (from Nikolaus), “spear strength”, “strong with the spear” (from Gerard), “from the town Gaeta” (from Cajetanus), in Celtic “spear bearer/thrower”. For girls, Kaj means “from the town Gaeta” (from Cajetana) or “pure” (from Katharina).