It is a male name of Latin origin. It means the large stone (strong or solid base). His apocope is Cayo. In Colombia cayetano means quiet, that it remains silent. It also means that it comes from Gaeta, the name of a village in Italy, in the Region of Lazio (so the original name is Gaetano).
Cayetano is incorrectly written, and should be written as "San Cayetano" being its meaning:
The Italian priest San Cayetano de Thiene is for the Catholic Patron Saint of Providence and the work. Temples which are you devoted all the 7 August they come vacant or unemployed to seek work, or those who succeed, will thank.