Quote Originally Posted by the Great Wikipedia
The console was known by the codename of "Revolution" until immediately prior to E3 2006. The suitability of the final name has been a subject of debate among some consumers and industry members. Nintendo spells "Wii" with two "i"s to imply an image of players gathering together, as well as to represent the console's controllers. Nintendo has given many reasons for its choice of name since its announcement; however, the most well known is:

Wii
Wii sounds like 'we,' which emphasizes that the 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.
There it is. I don't really think that they should have changed the name. I think "Wii" should've been the code name. But this makes sense I guess.