You have to let the authorities know if you move during your time in Denmark. The authorities will make sure your employer, doctor, bank etc. also know.
If you want to change your Danish address, you have to inform the authorities at life in Denmark via the below link. The online self-service is primarily in Danish but you can always get help to fill it in at Borgerservice (Citizen Service), at the library or maybe you know a Danish-speaking person who can help you.
You will need your NemID to use the online service. Also remember to bring your NemID if you want to get help at Borgerservice or at the library.
You must inform the authorities of your change of address no earlier than four weeks before you move and no later than five days after you have moved into your new home.
REMEMBER: If you leave Denmark for good, you also have to inform the authorities. Read more at lifeindenmark.dk about practical matters before leaving.
If you have questions about your move you are welcome to contact me;