Her name was Maria del Pilar Teresa Cayetana de Silva Alvarez de Toledo y Silva Bazan, and she was the 13th duquesa de Alba de Tormes, 11th duquesa de Huescar, 6th duquesa de Montoro, 8th condesa-duquesa de Olivares, 11th marquesa del Carpio, 13th marquesa de Coria, 9th marquesa de Eliche, 12th marquesa de Villanueva del Río, 6th marquesa de Tarazona, marquesa de Flechilla y Jarandilla, 11th condesa de Monterrey, 14th condesa de Lerín, 13th condesa de Oropesa, 14th Condestablesa de Navarra, 12th condesa de Galve, 14th condesa de Osorno, de jure duquesa de Galisteo, 11th condesa de Ayala, 9th condesa de Fuentes de Valdepero, condesa de Alcaudete, condesa de Deleitosa, senora del estado de Valdecorneja, senora de las baronias de Dicastillo, San Martin, Curton y Guissens. She was born in 1762 and lived to only 1802.
According to her Wikipedia article, "The Duchess died under somewhat mysterious circumstances in July 1802 at the age of 40. Although her death was ostensibly due to tuberculosis and a fever more colorful scenarios have been suggested over the years, including that she was poisoned. She had no biological issue although she did have an adoptive daughter, known as María de la Luz.
After her death, the title Duke of Alba passed to a relative, Carlos Miguel Fitz-James Stuart (1794–1835), who became the 14th Duke of Alba."
The present Duchess of Alba, the 18th, is named Maria del Rosario Cayetana Paloma ... Fitz-James Stuart y Silva. Why mention their names - so you don't look up either one as "Cayetana" - if you do, you will get citations for both the 13th and 18th Duchesses of Alba.