Based on a geocoded registry of more than four million residents of Santiago, Chile, we build two surname-based networks that reveal the city's population structure. The first network is formed from paternal and maternal surname pairs. The second network is formed from the isonymic distances between the city's neighborhoods. These networks uncover the city's main ethnic groups and their spatial distribution. We match the networks to a socioeconomic index, and find that surnames of high socioeconomic status tend to cluster, be more diverse, and occupy a well-defined quarter of the city. The results are suggestive of a high degree of urban segregation in Santiago.