After receiving your residence permit you will have to register at the National Registration Office with your new address to obtain your CPR number (personal registration number or civil register number).
The National Registration Office will also help you choose a family doctor in your area and record the name on your health insurance card, which will be mailed to you at home. 

Your family doctor is the point of reference for practically all medical needs of the family. Should you need a specialist, your family doctor is the person who should write you a recommendation in order for these visits to be covered by the state.

You are free to change your family doctor at any time should you wish to do so. To make the change you need to contact your local municipal office.