Cast your mind back to the old days, old days in console years anyway. When the Nintendo Switch was still a hazy dream among gamers, not yet come into fruition. When it did finally come out not so many predicted that it would go on to sell more than 114 million. But back then, before the Switch became official in 2016, it was known only as a codemane: 'NX'. Codenames are common among the console makers, and Nintendo have used 'Dolphin' for the GameCube, 'Revolution' for the Wii (which turned out to be true for that console), and 'Project Cafe' for the Wii U. Now we have discovered what Nintendo used internally for the NX logo thanks to a spot by Eurogamer (via Nintendo Life). Leaked online, the animated logo shows a while circle with a small dot inside it and the letters "NX" which are also in white over a blue background. The logo was used as the boot-up animation while the NX/Switch was still in development and known internally by its codename. The codename logo was discovered in a 2016 prototype for Mario Kart 8 Deluxe when the Wii U title was being revamped for the NX/Switch.
As for the Mario Kart 8 Deluxe prototype, a video of that exists too online. Being a port, the prototype looks pretty polished but there are some aspects of its build that are still clearly in development, with some art and assets missing. You can watch the prototype build, which dates from October 18th 2006, running on "real hardware" according to the description on YouTube here. Who knows how long the video will stay up considering how much Nintendo likes copyright strikes.
Who knows why Nintendo chose "NX" for the codename, the company has never revealed its naming conventions, but now we can see what the internal logo for the codename looks like. It's one for history to preserve.