What is this type of car called?

I remember my dad and/or grandfather calling a car like that a California Cruiser also, and they were both very into cars in the 50s/60s. I have not heard the term since then (since them calling it that, I wasn't around myself in the 50s/60s!) and I don't know where they got it from.

I know you're not asking, but unless the top is totally rotted, I don't think it's a great idea (but that's just me). And even if the top was totally rotted, I'd replace it before leaving it off. But your car!