"Microsoft" is still that company that makes operating systems and has that nerdy CEO. "X-Box" is where you go for the most advanced graphics on the console market.
MS worked day and night to establish "X-Box" as a gaming term, popular to both casual and "serious" gamers alike. I don't think it's much of a surprise that they don't want to start over.
As far as "360" goes, it might be similar to what Nintendo was thinking when they named the Nintendo 46. Maybe 360... megs... of something? 3.60 ghz procs?
iirc, the "no hard drive" thing was just a rumor. For a rumor it went pretty far, appearing on most game-related websites, so there may be some truth yet.