Zielinski is a very common Polish name, Which through migration is common in Germany as well. Zielina means simply "green". Zielinski might be simply a person who originates from a place like Zielina Gora etc.. However many Zielinski were part of the Polish (lower) nobility, the Slachta. In the middle ages many Jews in Poland were forced to become Christians and took the name Zielinski in Honor of the "Green Lady".
(Sent from Yasni user)