It is not possible to change your name when get married abroad if you live in Denmark. The Public Registration Office (Folkeregisteret) in your municipality must first register the marriage and you must then contact the parish you live in.
If you are a Danish citizen and live outside Denmark, you have to change your name in the country you live in.
You do not have to get a new passport or driver's licence when you change to your married name. They are valid until the date they expire.
However, you should make sure that the name on your passport corresponds with your name on a plane ticket, for example.
You will receive a new yellow health card after you changed to your married name.