I greatly doubt they're changing the name. They probably should but they won't.
I was pretty fond of "Nintendo Stream." It's different, easy to pronounce, and describes exactly what the console does. At the same time, considering Nintendo just stuck a 7 at the end of Mario Kart, "Nintendo 6" pretty much gets the point across. More than anything, while I kind of like how the actual console looks, they should redesign it because looks too much like the Wii. They might even want to consider launching a black or platinum model first to further differentiate it from the Wii.
EDIT: yes, I'm aware that there is a black model Wii, but the white case is clearly the most recognizable color.