Back in June 2004 there was already an article about Microsoft narrowing down the name for the next generation Xbox, today game rumor site Engadget claims they have a source confirming the "Xbox 360" name for the new Xbox (Xbox 2/Xbox Next/Xenon):

' Until Microsoft makes their official announcement on it, this one is still firmly in the rumor category, but we’ve gotten word from one of our trusted sources that Microsoft has pretty much settled on a name for the next Xbox: the Xbox 360. Our source, who has worked on several projects involving the Xbox and the Xbox 360, has seen the proposed packaging and other design elements for the new console, and says that as of right now the console is being branded as the "Xbox 360".
Apparently Microsoft was worried that calling their new console the "Xbox 2" would make it seem older or less "cutting-edge" than the PlayStation 3'