Yes, you're supposed to register within 14 days of your arrival, though you've sort of done that by getting your permits organised. Your commune wants to know you live there because they'll get a portion of your taxes of course.
They'll also have lots of rules and regulations they'll want you to learn about so you can live here like a good Swiss citizen does.
Seriously, yes they do want to know (for the tax side), but also they'll want to know that you've got your health insurance sorted, otherwise they'll try and put you on their own health insurance scheme which may be more expensive than yours. It's always worth making yourself known to your commune admin office.