You can find depth in anything though. In fact, apart from being deep on so many levels, the name is also wrong on so many levels.
You can't escape the fact that calling your console after something that is a slang term for urine is a bad move. You can say it's immature all you want - slang terms generally are immature, that's the point. Nobody is going to hear 'wii' as a noun and not think of 'wee' - c'mon. We don't use 'we' as a noun, but we do use 'wee' as one. Hence why everyone in the UK will automatically think 'wee' when they see 'wii'. (Plus, if you see it written down with two 'i's, you will automatically substitute them for 'e's when you get told how it's pronounced.) They would have been better off calling it 'wi' really, no matter what it stands for.
You don't have to like the fact that's how people's brains work, but you do have to accept that's what they will think. There's no point moaning about people making automatic associations - that's the whole point of good brand names. They make unconscious links to other things - hence 'wii' is probably the WORST NAME EVAR.