The marriage concluded in Denmark is immediately recognized in Germany.
The certificate of marriage which you receive in Denmark is recognized in Germany without additional legalization according to the bilateral agreement concluded between Germany and Denmark in 1936.
You do not need additional legalization for:
– foreigners authority;
– financial department;
– registration department (Bürgeramt, Rathaus);
– health insurance.
But you will most likely need legalization through the apostille if you:
– wish to apply for the name change after marriage;
– want to create a family book;
– are obliged to fly back to your home country (non-EU country) in order to prepare the documents for the family reunion.