The use of hereditary Jewish surnames was rare in Eastern Europe and the Imperial Russian Empire until the beginning of the 19th century. Jews were usually identified by their first names or by reference to the father, such as, "Isaac ben Abraham" (Isaac the son of Abraham). Sometimes Jews were given descriptive names such as "Moshe, the Pious One." The lack of surnames created administrative obstacles for the regime, especially in their tax collection efforts. In 1804, Czar Alexander issued an edict requiring Jews to take a surname and to use it in all transactions and registers. The edict was not rigorously observed and in 1835 more legislation was issued requiring the use of surnames. The Kahal (Jewish community government) was responsible for making sure surnames were assigned.
Joseph Korff, a grandson of Grand Rabbi Korff, related how the Korff family name was adopted:
"I was taking a course on International Relations at Brandeis [University] and someone distributed a pamphlet that listed Baron Samuel I. Korff as the author of an article on international relations. So I went home and asked my father [Jacob’s oldest son, Rabbi Samuel Korff] about it. He said that when the Russian state required Jews to take last names for the purposes of drafting them into the army, a German nobleman by the name of Korff[1] happened to be passing through their town. Since the Korff family were in effect royalty in their community, they took his name."
[1] Korff means "basket" in German, and people of German descent with this surname may be the descendants of basket makers.