Thank you! So if I read this all correctly, google will look for the links back to BlueWidgets.org on one hand. On another, google will also be searching the web to see if our corporate (brand) name comes up often. It is not like it is searching the text near (not in) our backlinks to see if our keywords are close too. Rather, google seems to judge the links and our brand mentions somewhat independently.
In that case, "BlueWidgets.org" might be good for our brand name if people easily and widely refer to us as "BlueWidgets.org". It doesn't really matter for our ranking if we have that space in the name or not, only that people use our brand name.
Put more simply, we don't get any extra SEO push if we make the keywords ALSO part of our brand name. The EMD is enough. Does that sound about right?
Thank you for the help. The article was good also. As you can see, I'm a beginner.