Whatever it's name is it cannot, for any reason at all, have the word Wii in it's name, or it'll be just like how people weren't able to realize the Wii U and Wii were separate consoles.
It needs a name that emphasizes power, or at least a name that will entice people to buy it.
Case in point, two of the greatest console names in history; Super NES and PlayStation. Both names emphasize how great their respective consoles were. It's the Super NES, because that's how much of a leap it was from it's predecessor. PlayStation says exactly what Sony's first console was for; A place to go to play popular games (Crash Bandicoot and Metal Gear Solid to name a few).
That's why I think the next Nintendo console needs to be called the Nintendo Storm (If they haven't been thinking of that name for something else already). Just read it out loud. It hides Nintendo's kiddie image, and evokes an idea of power and greatness. As long as Nintendo would release first-party software to back up the name, it would fit.
Well, time for me to shut up and let anyone else here say what they would name the next Nintendo console, and why.