Nave, or perhaps Pietronave -- Italy

My grandmother's maiden name is listed as Nave in various records from San Mateo and San Francisco Counties in California.  She was from the town of Varese Ligure, Liguria Region, in northern Italy.

She married my grandfather -- Pietro Toso -- who was also from Varese Ligure. 

I've wondered if its possible that her maiden name was shortened at some point from Pietronave, although I don't have any concrete information either way.

If you are researching the Nave surname in either the Bay Area or in Liguria Region,, please contact me.  I'd be happy to trade information.