I think they should go "full reboot" and just call it
The Nintendo
Ah yes, let's introduce the same problem the Xbox 1 did where when talking about consoles in a historical manner you have to be very specific to avoid confusing the latest console in the brand with the first one.
Sony totally got it right when they came up with a pretty decent name for their first console and then just numbered them sequentially after that. If Nintendo called the Super NES the NES2 and continued from there we wouldn't be having this discussion and I wouldn't at all be worried about what ridiculous name Nintendo is actually going to use.
Something with a noun would be a good idea. We've already got a "station" and a "box" so that's a convention people are used to. I really liked the Gamecube name, it's just unfortunate they decided to pair that with a purple lunchbox design. How about the Nintendo GameConsole?
That's a pretty meta idea and then Nintendo could sue competitors for using "game console" as a generic term.