"of Caieta"
The name Cayetano is commonly a male name from the "Spanish" origin that means "of Caieta".
Cayetano is the Spanish form of the Latin name Caietanus, which derives from the place name Caieta, the ancient name of Gaeta in Lazio, Italy, so the name means "of Caieta" or "from Gaeta". The corresponding Italian form is Gaetano. The name is borne by Saint Cajetan (Gaetano da Thiene, 1480 to 1547), a native of Vicenza.
The pronunciation of Cayetano is kah-yeh-TAH-noh.