Using millions of historical census records and modern birth certificates, we document that immigrants assimilated into US society at similar rates in the past and present. We measure cultural assimilation as immigrants giving their children less foreign names after spending more time in the United States, and show that immigrants erase about one-half of the naming gap with natives after 20 years both historically and today. Immigrants from poorer countries choose more foreign names upon first arrival in both periods but are among the fastest to shift toward native-sounding names. We find substantial cultural assimilation for immigrants of all education levels.