"... Padilla is a Spanish and Portuguese name, also spelled Padillo, being one of those names derived from the place where a man once lived or where he once held land. There are two places by the name of Padilla in Castorgeriz in the Burgos region of Northern Spain. The surname Padilla is derived from these places, the one being Padilla de Arriba and the other Padilla de Abajo. It was used, at first, as a convenient method of identifying one who hailed from either of them. Today, the family name Padilla are found all over the world due to migration." from https://www.geni.com/projects/Padilla-Family-of-the-Philippines/647

The Padilla family is one of the original Spanish settler families of New Mexico but the surname is also common elsewhere. Many of the New Mexican Padilla families are descended from Jose Padilla (son of Diego Padilla) who was born 10 Sep 1649 in Queretaro; died 1712 in Guadalupe del Paso, New Mexico. 

There is also a Padilla family in the Phillipines with a project at GENI.com  - see https://www.geni.com/projects/Padilla-Family-of-the-Philippines/647

The Denver library has placed a document, a PDF file: Descendants of Diego Padilla and Luisa dela Serna By  LaDeane Miller which lists all of Jose Padilla's known descendants until the mid 1800s online here: http://digital.denverlibrary.org/cdm/ref/collection/p16079coll18/id/64450