Richard Andree's 1881 map of the Jews of Central Europe
Ashkenazic Jews were among the last Europeans to take family names. Some German-speaking Jews took last names as early as the 17th century, but the overwhelming majority of Jews lived in Eastern Europe and did not take last names until compelled to do so. The process began in the Austro-Hungarian Empire in 1787 and ended in Czarist Russia in 1844.
In attempting to build modern nation-states, the authorities insisted that Jews take last names so that they could be taxed, drafted, and educated (in that order of importance). For centuries, Jewish communal leaders were responsible for collecting taxes from the Jewish population on behalf of the government, and in some cases were responsible for filling draft quotas. Education was traditionally an internal Jewish affair.