Using millions of historical Census records and modern birth certificates, we document substantial immigrant assimilation into US society. Both in the past and the present, immigrants choose less foreign names for their children as they spend time in the US, erasing one-third to one-half of the names gap with natives after twenty years. Less educated immigrants and those from poorer countries start out with more foreign names but are fastest to shift toward native-sounding names. Other measures such as intermarriage and citizenship applications also point to meaningful assimilation. Immigrant children with foreign names had worse economic outcomes and married less-assimilated spouses, but these differences disappear within brother pairs, suggesting little penalty from names themselves.