The rules for residence and work permit vary, depending on your country of origin and whether your stay is shorter or longer than three months. See the Welcome guide from Workindenmark.dk, and newtodenmark.dk for details.
Relevant contacts for registrations:
Citizen Service (Borgerservice)
Citizen Service (Borgerservice) in Herning helps you to register at the national registration office (folkeregistret), get a civil registration number (CPR-nummer), choose doctor, get MitID and Digital post.
Citizen Service (Borgerservice), Torvet 5 (Entry B), 7400 Herning, +45 96282828.
You need to bring your residence permit, and to show up in person. You can book an appointment and see opening hours here.
If you move internally in Denmark you need to register the new address. This is done digitally or by contacting citizen service. Please use Notification of change of address online.
Please note! When you are leaving Danmark, it is important to notify that you are leaving your address and de-register from CPR.
Tax
When you work in Denmark, you must also have a tax card. Apply for it online.
Read all about your Danish Tax Affairs on Skat's page in English.
Residence permits
EU and Nordic countries, contact: SIRI Aarhus, Dokk1, Hack Kampmanns Plads 2, 8000 Aarhus C
Other countries: Contact Danish Agency for International Recruitment and Integration, phone +45 7214 2000.
International Citizen Service in Århus
International Citizen Service West in Århus can help with the same tasks as Citizen Service in Herning, as well as residence permits in the same office.
International Citizen Service West, Dokk1, Hack Kampmanns Plads 2, 8000 Århus C, phone +45 7222 3375.
Note that you need to book an appointment for CPR-registration at ICS West.