No, it absolutely isn't if we are talking about becoming #1. The name "Xbox" has a certain image attached to it and a new console that launches with this name (let's say Xbox 720) automatically carries that image over, whether or not it would still hold true.

"Xbox" doesn't have the image to get widely popular, thus preventing it from becoming #1. So in order to win, Microsoft has to kill off their Xbox brand.

I can't entirely disagree with that conclusion, but you have to realize that the gamers who think that way are a minority. There are lots of gamers who think in a negative way about "Xbox" and then there is a huge amount of people who are completely indifferent to "Xbox" and would never ever consider to touch such a thing.

In case MS names their next console again Xbox something, the people who think that "Xbox = cool games" would most likely buy it, but on the other hand you have much more people who wouldn't buy it because the name of the console alone would reinforce their negative prejudice about Microsoft's system.

Why do people keep refering to it as the 720?

You're nuts if you think that. Japan will be a 20 - 30mil sales for first place console there. It would be hard for anyone to make that difference up.

And if the console is selling that well in japan chances are its selling just as good in other regions. Even if MS has the lead in those regions it wouldn't be a 10-15mil lead.

It's not just RRoD, there's much more to it. The image of the first Xbox prevented the 360 from selling better as well. What was that image? The Halobox or the shooterbox, mainly because the biggest exclusive games for the Xbox were FPS games and there wasn't much else that stood out.

The 360 still couldn't get fully rid of the image of being the shooterbox although the variety of genres did improve compared to Microsoft's first console. Nevertheless, a lot of people see the 360 as a console that is heavily catering to American tastes which explains the mediocre sales in Europe and the horrible sales in Japan. A lot of the best games for the 360 are available on PC and/or PS3 as well, that doesn't help either.

Another Xbox system would have to overcome the image of being a console for Americans AND being an unreliable system. Certainly these things won't prevent 360 fans from buying Microsoft's next system, but how high are the chances that people who dislike or don't care for the 360 would buy the next Xbox?