We observe a marked increase in the spatial homogeneity of the popularity of first names across the United States in recent decades. We explain this by calibrating a modified standard model of neutral cultural evolution to the record of first name popularities for the United as a whole since 1900 and across the individual states over the last 50 years. We obtain estimates of both the temporal and spatial diversity of the speed of cultural evolution during the 20th century and early 21st century. We find that the speed of innovation of popular baby names accelerated substantially since the end of the 20th century. We suggest that the increased inventiveness has driven a drift process that increased the geographic diversity across the United States.