Just about every videogame site is reporting this. Plus it is can also be found at nintendo's official website.
Here's what Nintendo says:
"Introducing ... Wii.
As in "we."
While the codename "Revolution" expressed our direction, Wii represents the answer.
Wii will break down the wall that separates video game players from everybody else.
Wii will put people more in touch with their games ... and each other. But you're probably asking: What does the name mean?
Wii sounds like "we," which emphasizes this console is for everyone.
Wii can easily be remembered by people around the world, no matter what language they speak. No confusion. No need to abbreviate. Just Wii.
Wii has a distinctive "ii" spelling that symbolizes both the unique controllers and the image of people gathering to play.
And Wii, as a name and a console, brings something revolutionary to the world of video games that sets it apart from the crowd.
So that's Wii. But now Nintendo needs you.
Because, it's really not about you or me.
It's about Wii.
And together, Wii will change everything."
Games Are Fun article
Nintendo Wii offical site
Personally I don't like the name at the moment...but maybe it will grow on me.