Moniz is a Portuguese name.Most of the Portuguese that immigrated to Hawaii in the 1800s were from the Azores.The Azores are Islands in the Atlantic 'owned' by Portugal.Most of the immigrants came to Hawaii to work on pineapple plantations.The most common areas for people from the Azores to immigrate to seem to be Hawaii, California and Massachusetts.
The people of the Azores are not strictly from the country of Portugal originally.It was a little like the US, where people of various European countries came there. Many of my Portuguese family are blond or red-heads and have blue or green eyes.
Many people with the name Moniz changed the spelling when they came to the US, probably to fit in.
Have you tried to get your grandfather's death certificate from California?If the person who reported his death knew his parents names, it would be on the certificate.I believe the California death records are also online (rootsweb or ancestry?)