I found this site in the SE community list. I had to visit the site because the name wasn't descriptive enough to tell me what it was about, and when I did, I was half expecting to end up on a site about alternative lifestyles.
The argument from SeniorShizzle that "90% of Apple's users over the age of 18 would recognize [the Think Different] slogan immediately" is dubious at best, and at worst it excludes entire geographic regions where the ad was not campaigned, new users, users of Apple products that were not advertised with the "think different" slogan, and generations of users to come. I'd argue that the name is esoteric. And while there are problems with the name "Ask Apple" as discussed in the comments, that doesn't mean there is not a problem with the name "Ask Different".
That being said, I'm not here to support a name change, I'm just offering my two cents on this topic. And while I haven't been a member for very long, I have a different theory as to why the name might have stuck (and why it might be a good match), according to something I remember being told by an old business professor I once had.
According to him, Apple's success has always been fueled by those evangelist users who embrace the fact that Apple is not Microsoft, and historically has never been "mainstream". These users want to be different and feel like they're exercising their right to choose. Perhaps they perceive themselves as the crazy ones. The misfits. The rebels. The troublemakers. The round pegs in the square holes.
And that's why "Ask Different" is arguably a pretty good name choice for the community here.
But alas, I'm just a passerby.