We develop a novel methodology to analyze intergenerational social mobility over long period of times when the precise ancestors of the individuals cannot be identified. Our approach is based on the incorporation of surnames in the analysis of social mobility. We apply our methodology to asses the degree of intergenerational social mobility within two Spanish regions from the late 19th century to the beginning of the 21st century. The results show that the probability of having a high education level, or belonging to a high status socioeconomic group, still depends on the socioeconomic status of the great-great-grandparents. However, our analysis suggests that such dependence will vanish in the next-to-present generation.