I mentioned this in the sibling comment, but it still doesn't seem possible. Who's determining these social class tiers? Black people? White people? Either way, there's no way to control for the status as the names themselves are already indicators irrespective of the social status.

In other words, you're trying to separate racism from classism, but race and class are already inexorably linked to begin with. Any perception of class to the name would already be influenced by historical racism, for better or for worse.