The Spanish surname Rios was originally "de los Rios," or "of the rivers." The family coat-of-arms depicts this. The name is found mainly in the south of Spain :
The red spots indicate a higher incidence of the last name Rios in Spain.
Spaniards named de los Rios or Rios moved to Latin America (Mexico, Peru, etc) and from there to the Marianas and the Philippines.
In the Marianas, there was a Rios family from the early part of the Spanish conquest. In the 1727 Census, there is a Sergeant Francisco de los Rios. He is listed among the "Spanish" troops, but that can also mean he was from Latin America, where many people had mixed blood (Spanish and native). Francisco married a Chamorro woman, Rosa Taihimas. "Tai" means "lacking, without," and we don't know what "humas" means. "Humas" would become "himas" if "tai" goes before it.
They had a son and three daughters, and maybe more after the census was taken.
There's also, in the same census and Spanish, a Miguel de los Rios, married to Marcela de la Cruz. There is no indication what connection, if any, Miguel has with Francisco. They, too, had children.
Then there's a third Rios, also Spanish, named Juan Antonio de los Rios, married to Josefa de la Cruz, of unknown connection to the others. They had at least four sons (and a daughter) by 1727. Plenty of Rioses to keep the name going. Rioses show up again in the 1758 Census.
1. Felipe Rios. From Hagåtña. Possibly the son of Vicente Rios and Josefa de la Rosa. Married Rosa de los Santos, and after her death, Antonia Megofna Salas.
2. Brigido Rios. From Hagåtña. His mother was a Filipina with the last name Ayuban. Married Josefa Garrido de Leon Guerrero. Their son Jose was a Guam educator and businessman for whom Jose L.G. Rios School is named.
3. Benigno Castro Rios. From Hagåtña. Married to Gregoria Campos de Leon Guerrero. Now one of Benigno's sons, Casiano, has Ayuban as a middle name. So Gregoria is possibly the 2nd wife of Benigno, and that Benigno is the father of Brigido in #2 above.
4. Vicente Rios. From Hagåtña. Married to Josefa Cepeda.