Most providers in Denmark provide the option of continuing with your old telephone number when you switch onto a prepaid SIM card. You just have to mention the current number during the registration process to transfer it over.
You can easily top up your prepaid SIM card online through the website of your mobile provider, through their mobile application, or at various retail chains throughout Denmark. Most providers allow flexible options for topping up: you can choose the amount and to which services among data, calls, and texts the refill should be applied.