NaNoWriMo is, you are correct, the name of that organization, which has always run the competition known by that or the longer version of the name.
The competition, however, came out of a viral movement of one month novel writing, which was independently pursued by online groups, promoted by libraries, and generally had nothing to do with the office of letters and light or its "national" novel writing month, except in their being inspired by/a focus for that already existing movement.
I apologize for my imprecision. I was and am mad at them. Their being "a nonprofit" does not mean they aren't capturing a pre-existing movement and channeling it into money and other benefits for themselves. They did, technically, start the well known "national novel writing month," now shortened to NaNoWriMo. Despite actually being international from the beginning, they had a catchy name. However, it's not even a catchy name they invented. It was taken from a concept that was present in the zeitgeist, and they promoted their version of it to the point that the original movement coalesced pretty much only on the focus of their competition.
Kind of like how itch.io didn't invent game jams, it is just the host for a lot of them, but for something more niche (since fewer people want to speed write a novel than bang out a small practice game quickly).
I only have my memory to go on here. I can't give a solid timeline, but by the time in 2005 or 6 (depending on which website one checks) that the nonprofit was founded, the practice had been around for several years. I remember encountering the idea while I was in community college in 2001.
Having grabbed all the attention for themselves, I blame them for multiple problems, but the most relevant one here is: they gave themselves a megaphone, and used it to spout bullshit that uses disability like a human shield while actually harming the interests of actual disabled people. So not only failing to use their platform to spread a necessary truth, but spreading toxic filth instead.
People should go back to self mediated novel writing challenges. NaNoWriMo was a mistake.