I initially thought the name was a bit pointless and cheesy myself, but then we're not the target, the mass user market is. They don't analyze and overthink these things like we do, instead they just accept the information and such a catchy 'thought' helps to lock-in the memory.
Since the entire purpose behind search is to find something, applying relevance to results makes complete sense and the categories in the left hand pane of Bing help organize the results in meaningful ways. I originally used Bing to find the image linked above, but then floundered my way through Google looking for the same, with much less organized and thus understandable results.
With Google, I find myself trying to ignore much of the displayed page precisely because most of the sponsored and/or actual results are either useless or even dangerous. This is completely counter to my original reason for performing a search, to simplify my path to discovering something. Google has the results, they've just reburied them in their own generated trash, what a foolish move!
Though as an analytical person the 'Bing' thought wasn't the first thing that occured to me when I saw a preview last week, it now makes sense when I think back to the eureka moment(s) that occured during the demo.
For these reasons, I now consider Bing an appropriate name and actually wonder why we were required to accept the idea that to 'Google' is to search for something?
Microsoft has a significant uphill battle in the quest for penetration of the search market, but I have noticed a renewed sense of innovation and excitement across the entire orgnization over the last few months resulting in many significant improvements in their products which will only serve to benefit the consumer.