Nembei and Natsy reference

They are not Nikatsu and Naoyasu as animals

These animals are their Nakamihi ancestors who were reborn temporarily as animals when they were in need for spiritual help. What you would call a familiar, perhaps.

Nembei, the bunny, and Natsy, the cat, don't remember any of their past lives details like their real names or such, because they were only reborn with their big knowledge of the real meaning of life. They do however recognize the Nakamihi family as their own, but just as a feeling rather than a memory.

Nembei and Natsy are nicknames Naoyasu and Nikatsu gave them respectively, as to avoid confusion. But they insist that they really have no names and that's just a people thing, as to feel a sense of identity.

The accesories they use are given by each twin. Hence the similarities to their respective favourite colours.