From an online professional forum:

The Wii is an awful name.

Wii for an entertainment platform is no more awful than Yahoo! for a search engine, Google for an online ad agency, Twitter for a microblogging service, and Alltop for a blog directory. Wii, however, is arguably more potent than many of those names.

• Wii is playful. You can do things with Wii that you can't do with International Business Machines. "Would you like to play with my Wii?" The derivative is great, too. "Touch Mii." There're also "Wii win" and "I'm just a Wii lad."
• Wii is happy. You can't help but smile when you say Wii aloud. Smiling does have a psychological/physiological effect. Do you smile when you say American Institute of Certified Public Accountants? How about The Institute of Internal Auditors? I didn't think so.
• Wii is eye-catching. The only other word with the letters "ii" that you might see in a shop window is Hawaii. Subconsciously, you can bet that there's some association going on there. Who doesn't want to go to Hawaii, right?
• Wii is one-of-a-kind. Xbox 360 says, "I'm too sexy for my chassis." PlayStation 3 says, "For the third time, I am the one-and-only total home entertainment center!" Wii says, "Unlike everyone else, I'm not a sequel!"

There are more reasons why Wii is not an awful name. Wii is an absurd name though. And that's okay.

PS. "IBM. UBM. We all BM for IBM." But that's not nearly as cool (in certain circles.)