A rivera, in Spanish, means "brook," or "creek." Not quite a river, which is río.
There are no Riveras in the earliest censuses we have, the 1727 Census and the 1758 Census.
Yet the Rivera surname shows up in fair numbers in the 1897 Census. Sometime after 1758, a Rivera, or perhaps 2 or 3 Riveras, whether relatives or not, showed up on Guam and started families. Who they were; what ethnicity they had, is anybody's guess at this point. The name is Spanish, but Spanish surnames can be found among South Americans and Filipinos.
The oldest Rivera in the 1897 census is Don Luis Rivera of Hagåtña, aged 88 in 1897. He was married to Juana Pangelinan.
Another elderly Rivera was a woman, Rufina Lujan Rivera, aged 65, also of Hagåtña. She married Tiburcio Arriola.
Manuel Rivera, aged 72, of Hagåtña, was married to Ana de Leon Guerrero.
Jose Rivera, aged 74 of Hagåtña, was married to Maria de Leon Guerrero.
These last two have my suspicions aroused, especially since they're just a few years apart. It was not unusual for two brothers to marry two sisters, but until we find better evidence, we better not jump to unfounded conclusions.
Finally, we have the Agat Riveras, descendants of Jose Rivera, aged 57 in 1897, married to Josefa Delgado.
WORLD FAMOUS RIVERAS