Google essentially did open source Chrome. The reason for the different names is quite important: anyone can modify and build Chromium, and that's the great benefit of open source, but it also carries a risk: you don't know what changes were made unless you trust the source or built it yourself. The official Google Chrome brand means it's an official Google build of the browser, so you know you can trust it if you trust Google.
The other differences are just for legal reasons, we can't include certain code (like Flash) in Chromium because we don't own it. As you can see by this announcement, we are committed to open-sourcing as much of Chrome as we can, and this is a big step in that direction.