Of course, we tried to set them straight, but the conspiracy theory persisted -- as conspiracy theories are wont to do -- and now, with the help of the United States Patent and Trademark Office, we can see that Nintendo has indeed registered the name "Wii" with no fewer than nine applications!
The trademark applications were filed on April 27 (the day the name was publicly announced), but have a "priority date" of November 11, 2005, meaning they had decided on the new name as far back as November of last year and delayed the trademark registration, lest the proverbial cat be let out of the proverbial bag.
The trademarks cover the use of the name Wii in applications ranging from "printed matter" like iron-on transfers or, who knows, console packaging to "clothing" like wrist-bands or, perhaps maybe, t-shirts. They also cover "watches containing a game function", "providing temporary use of non-downloadable video game programs provided via the Internet", and about a thousand other things, meaning there's a wealth of info to be misinterpreted here by the fan community.
You'd better put your tinfoil hats back on...let the crazy theories commence!
(Update: Added links directly to the Trademark Document Retrieval system. Thanks Me Here!]