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.

The previous answer is correct. I would like to add however, that first names do have some of those meanings. To list a few: Simcha ( happiness); Nisim (miracles) Gila (rejoicing) Rina (jubilation) Ditza (pleasure) Chedva (delight) Shira (song)

I think that you have been misinformed here. Jewish surnames are no different from family names in any other cultural or national group: they typically refer to the place where an antecedent came from, or the name, or the profession of an antecedent. What is more, surnames generally have no significance within Jewish culture. The use of surnames was usually imposed by the authorities of the country in which they lived, and when people emigrated they often changed their surnames according to their new country of residence.