The December 13, 1966 Second Revised Final draft of "Space Seed" consistently spells the name as Noonien.
Okay, then. That suggests that Bjo Trimble misspelled it in the Concordance, and that misspelling became an encyclopedic error when it was quoted in other sources (as occurred with other Concordance errors such as giving Dr. Boyce's first name as Joseph, and with Okuda Encyclopedia errors like "Neela Darren" and "ShirKahr"). But somewhere along the line, it was determined that "Noonien" was the correct spelling, and that's what's been used ever since.
Meanwhile, in my ongoing search for the origin of the name "Noonien," I decided to try some alternate spellings. I thought I had a lead when I got results for "Nunien" as a Latin word, but it turned out that was Google Books' OCR system misreading numen (and in one case flumen). Clearly some bugs in that system. I found a couple of references to "Nunian" as a Welsh surname, as well as "O'Nunian," which is apparently Irish. (And it was looking like there was a "Nunian calendar," but that's apparently another Google Books misreading -- for "Numan calendar" -- that's already metastasized to other sites. More encyclopedic error.)
Ahh, here's something: "Nunia" is apparently a name found in India, as a surname, a place name, or a feminine given name. (It's no doubt coincidence, but I found a Classmates.com page for a high school whose alumni/ae include a Kim Singh and a Nunia Singh.)
So I suppose it's possible that "Noonien" could be a variant spelling of a variant name, maybe a masculine counterpart of "Nunia."