Surnames question - Ruis de Esparza from Teocaltiche, Jalisco

Hi,

I'm hoping to figure out the last name of Jose Antonio Claudio Ruis de Esparza and of Maria Gonzales Bermejo, both found here:
https://beta.familysearch.org/s/recordDetails/show?uri=http%3A%2F%2Fpilot.familysearch.org%2Frecords%2Ftrk%3A%2Ffsrs%2Frr_585506652%2Fp1&hash=HloWXpZgU9zB10k5M56iYku8TUc%253D

All subsequent records for the former are "Antonio Esperza". But his father and grandfather are "Ruis de Esparza" so I can't figure out whether "Ruis de Esparza" is a full last name or the combination of two last names. Looking at the families in the above record doesn't give any clues.

Also I can't figure out the surname(s) for Maria Gonzales Bermejo. It seems that both last names are used together in reference to her father, rather than father and mother.

Does anyone have any insight into these families in Teocaltiche area?

Thanks, Arturo