It is my understanding that many European Jews had no fixed 
patronymics. They were using the traditional system of using 
the given name of his/her father: Samuel ben Jacob or Sarah 
bar Jabob would be the children of Jacob. Samuel's son would 
be "ben Samuel." Napoleon as part of his decrees across the 
empire in the early nineteenth-century imposed a system of 
fixed patronymics. Poland instituted official fixed state 
names in 1821 and Russia in 1844. People chose a range of 
arbitrary names--their village, natural objects (rose, stone, 
mountain) for registration with the state, while thinking of 
the traditional naming system as their real name. Therefore, 
several generations later, they arrived at Ellis Island, once 
more they had to formally register with the state, and chose 
some other symbolic name--for instance, "Eagle" or willingly 
Anglicized their former state name. Their "real" name 
remained the same.

Cheers,
Trish