If it tastes like a California Common, then it *is* a California Common.
I'll admit, I almost ranted about how it would need to be a lager yeast fermented warm in order to be a true California Common. But then I thought... well, S-04 tastes like a lager to me, and BRY-97 (M44) is quite clean as well, so.... it will probably still fit the bill. I mean, if you tasted Anchor Steam and your two beers next to each other side by side, blindfolded... would you be able to tell us for certain which one fit the style best, which one worst? If not, then they can all pass for the same style. But if one or two of them are WAY out of whack, then you would have to decide whether it fits another style better. IF that even really matters to you, which, by your question, I would suppose that it does.
Call it what you like. If it's reasonably close, you can call it the style you intended to brew. If not, then you can read up on style guidelines to see where else it might fit. Closest other style might be American Amber Ale. Or maybe Altbier. Something like that. Pull out the guidelines and see which one it resembles most closely.