Several books and articles indicate that Osip Volkov defected from a Russian ship at Monterey around 1815, midway through the Mexican War of Independence. Naturalized as Jose Antonio Bolcof, he served as alcalde of Branciforte. The Russian-American Company had a royal monopoly on the fur trade in America. What was the ship on which Volkov arrived in California?
According to pg 317 of the Book California Through Russian Eyes, by James R Gibson,
...while hunting sea otters from the Ilmena, he either jumped ship or was captured by a Spanish patrol.
The Ilmena is listed as 'purchased from the Americans' on the Russia-America Company wiki page.
So there's your ship name, and yes he was employed in the fur trade.