If you were born in another country than Denmark, your local registrar who is responsible to process and register the civil registrations for you is the parish close to where you live.
However, there is one thing that is different when you are born abroad.
If your name is incorrect, or a name is missing
If your name is incorrect or a name is missing on your identification card or on letters from public authorities, your name can be corrected.
If your name is incorrect but has not been changed in Denmark
If you have not had your name changed in Denmark, you should contact the authority that registered your name in the CPR-register at your arrival to Denmark. The authority may be the Danish Immigration Service or Borgerservice (Citizen Service Centre) in a municipality.
You must bring proof of the correct spelling/missing name and ask them to correct the name.
If your name is incorrect but has been changed in Denmark
If you have had a change of name in Denmark, you should contact your local registrar. They can help you correct your name.