As silly/awesome as you think the name "Wii" is, at least it has a meaning. "We". Togetherness. But what about the "DSi"? What does that mean?
You could say it's got something to do with having two cameras, but then, according to Nintendo of America's David Young, it means your DS is "individual". Here he is explaining in detail:
The DSi is really about the "individual" gamers. For instance, the Wii console is really meant to be a shared experience for families and friends, where even while you can share pictures and share the fun with multiplayer on the DSi, it's really designed to be an individual experience. My DSi is going to be different from your DSi — it's going to have my pictures, my music and my DSiWare, so it's going to be very personalized, and that's sort of the idea of the Nintendo DSi. [It's] for all of the users to personalize their gaming experience and make it their own.
He could have said "because the only thing different about this and tens of millions of other DS handhelds are two small cameras and a higher price tag", but then, he'd be pretty sucky at his job.