Yes and no. Surnames were definitely imposed, but very often people chose their surname and woul pick the home town (Posner from Posen, Minkowitz from Mintz), those connected to their ethnicity (almost all Cohen's, Kohen, and Katz's are from the priestly tribe, and almost all Levi, Levy's etc are from the Levite tribe), related to religion (Israelovitz means son of Israel) or described the profession, such as Goldsmith (dealing in gold) Saltzman (dealing in salt) Shreiber (a writer, or probably a scribe). Baum is a very common name and means a tree (boim is a tree in Yiddish)...there are many examples.