Azaeleagen - from Greek, this translates roughly as "Earth emerging from the dryness". Latinized, it could be more like Azaeleaca, Azaeleacia, or perhaps Azaeleca or something.
Some rumor starts that there are one-eyed men in the interior, maybe up in the mountains. People start speculating that, like the legendary Arimaspi of Herodotus, they war with gold-guarding griffons. The rumor takes hold in imagination and the land becomes Arimaspia.
California's a big state - there's no guarantee that it'll all be one region like OTL. You could easily use multiple of these names in the same TL for different regions.