The National Register (Folkeregisteret)
If you are going abroad for less than 6 months and you maintain your accommodation in Denmark, you can keep you registration in Denmark. In that case, however, you are not allowed to sublet your room.
If you do not maintain your room or if you go abroad for more than 6 months, you will need to inform the National Register (Folkeregisteret). When you return to Denmark you will need to register again.
A study period or internship abroad might affect your tax situation in Denmark. For more information click here.
You should always check the travel guides by the Ministry of Foreign Affairs of Denmark (Udenrigsministeriet) as they will be updated on the latest developments in the country where your study abroad period will take place. You can access the Ministry's travel guides by clicking here.