You'll see both. I believe JBoss Seam is the official name, but it's no more JBoss specific than Drools (now JBoss Rules) or Hibernate. It just happens to be (mostly) written by people that are employed by JBoss.
In forums you'll probably most likely see it called simply Seam.
Of course, while writing a book the world changes. The original name of the project was "JBoss Seam", in the same way that you have "Apache Tomcat". Since then, the project has officially become just "Seam". Of course, it is still hosted in JBoss labs and sponsored by JBoss, so it is not wrong to call it "JBoss Seam".
As for the comment about the application server, I want to dispel a myth here. Previous leaders of JBoss screwed themselves by letting people associate JBoss with the application server. JBoss is now a middleware company and sponsor any type of project that might be used in a middleware platform. The application server is one small chunk of a very large platform, maintained and developed at jboss.org. The word "JBoss" has nothing to do with an application server. The application server is JBoss AS. I took extreme care in the book to always qualify the application server as "JBoss AS".
Btw, JBoss is a pretty darn cool company. I was one of the folks who didn't like them very much in the beginning, but I now believe that they have some of the best open source software in the entire Java space. Sure, they still have a lot of developers whose voices can be pretty sharp, but that doesn't diminish the fact that they are creating great software.