I was wondering if there is a connection between Canis and German Kaninchen (Rabbit). It seems not. Kaninchen is Kanin plus diminutive -chen form and comes from Cuniculus. In dialect Kaninchen are called Karnickel which seems to be closer to that root.
German Hase (hare) seems to be based on some proto-european word for grey which would be canus in Latin and seems to mean white and yellow in other languages (wtf) which would be weirdly close again, but not the same root...