The name of the city is Berlin, Berliner is the genitive (or an inhabitant of Berlin) - so it's either Dynamo Berlin or Berliner FC Dynamo. Anyway, Dynamo plays in the 4th division Oberliga Nordost-Nord, Sachsen Leipzig plays in the Oberliga Nordost-Süd (4th division as well). The other big club from Leipzig, Lok, plays in the lower divions - 11th level last season.
After rereading my post I have to corect myself: Berliner isn't the genivtive but an adjective - the genitive would be Berlins. Damn, I suck at grammar .