Assuming the dog is registered in your name, and you acquired the dog before 1 Sept. 2008, you are not required under the new federal legislation to attend the obligatory training courses. (Sachkundenachweis in German.)
But if you were to acquire another dog (after 1 Sept 2008), you would be required to take the practical classes with that dog.
Note - Ownership is individual, not familial. My dogs were imported here under my name as owner, registered with ANIS and the Gemeinde before 1 Sept 2008 under my name. Therefore I am not a new dog owner, and am excused from the theory classes. However, my husband - although he has shared 20 years of dog ownership with me - has no similar paper trail. So, were we to decide that our next dog goes in his name, he would indeed be considered a first time owner, and be expected to take the theory as well as the practical class.
I adopted another dog after the law came into effect, and so am required to take the practical course.
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I would strongly encourage you, however, to attend some kind of training class, perhaps a Familenhund class or a sports class, as an opportunity to learn more about the ins and outs - and expectations and obligations - of dog ownership in Switzerland.
Not to mention, the right training class can be great fun for you and your dog - and a very good way to meet new friends.
(I found my feet here in Switzerland largely through my dogs.

)
Best of luck to you as you and your pooch settle in here.
ETA: I am referring here to the federal law - cantonal laws might or might not also apply. After I get back from walking the mutts, I'll have a look at Luzern regs.