It seems, though, that most Jewish names (inside Austria-Hungary at least) were arbitrarily given. See this quote:
In some countries, such as the Austro-Hungarian Empire, Jews were forced to take surnames with a German appearance, and they usually could not choose them. These arbitrary family names have no relationship whatsoever with either the trade or craft, nor the physical description, nor the geographic origin of the person so named. We have already quoted SCHWARZ, WEISS, GROSS, KLEIN, and ROTH. But there are also a long series of names formed with two German roots such as MORGENSTERN, MORGENSTEIN, APFELBAUM, BIRNBAUM, ROSENBERG, ROSENBLUM, ROSENBAUM, WEINBAUM, WEINBERG..... Note that the spelling of these names varies considerably, especially when they transited through Poland or Russia.
[from an old article on genealoj.org]
It seems like also Napoleon had opinions on Jewish names.
Quote:
When the French emperor Napoleon Bonaparte overran all of Europe including Germany and Poland, he decreed that all Jews must adopt modern European names as first demanded by the French revolutionary (1789) government. Thereupon the Jews of Europe adopted many geographical names such as Rosenberg or mountain of roses, Goldberg or Silverberg or Lilienthal or valley of the lilies. If a Jew did not adopt such a name, then the state chose a name for him. This led to such names as Goldstein and Rubenstein and Silverstein, all connoting precious stones which, according to anti-Jewish sentiment, were all hidden in every Jewish home because “the Jews had all the money” (If we Jews had all the money, everybody would convert to Judaism this day).
http://www.jbuff.com/c120502.htm