In societies where surnames are inherited from parents, we can use these names to estimate rates of intergenerational mobility. This paper explains how to make such estimates, and illustrates their use in pre-industrial England and modern Chile and India. These surname estimates have the advantage that they require much less data than traditional parent-child estimates. They are also more robust to errors in status data. Thus, they can be used to estimate social mobility rates in early societies such as England 1300-1800, or in less-developed societies now. Surnames measure a different aspect of social mobility than conventional measures, but this surname measure is the one that matters when we consider group-level convergence of social status, or the time needed, measured in generations, for any disadvantaged groups to attain at least average status. Surnames thus allow us to measure a key element in the multigenerational mobility process.