As far as I am aware Cajétan is French, and is a form of Gaétan (also used in the French Language); I have two ancestors; a father, Charles dit* Gaétan dit Cajétan dit Charlitte Saulnier, and son, Cajétan Saulnier who were alive in the mid and late 1700s in Canada; their ancestry was Acadian French; their ancestors having come from France in the 1600s. (*dit is French shorthand for 'nickname'/known as/called).
(Source: https://en.m.wikipedia.org/wiki/Saint_Cajetan) [noted -ed]