Every solar power system connected to the electricity grid must be registered with the grid operator. For smaller systems, this is very easy: You can simply fill out the registration on www.energieleveren.nl. Your grid operator will be notified automatically, and you won’t need to take any further action. Registration is important because the grid operator will check whether your household electricity meter is suitable for feeding energy back into the grid. If it isn't, they will need to install a new meter.
Zonnefabriek will usually take care of this for you.
Additionally, you can inform your energy supplier that you are installing solar panels. They can then calculate a new monthly payment for you. However, this step is not mandatory. After a year, your energy supplier will notice that your energy consumption has decreased and that you are feeding energy back into the grid. They will then automatically adjust your monthly payment accordingly.