The problem isn't with the project name. We could just as well call it the "Microsoft Windows and Red Hat Watson Interpreter Java Enterprise" project. As long as it's an internal name (for a loose definition of "internal"), then it's our problem, "Language cannot be trademarked" and all that.
The issue is that we need a trademarked brand to use for the product. And for that, we can't use anything that's already trademarked by somebody else. That includes Java, Java SE, Java EE, Java ME, J2SE, J2EE, J2ME, and any other variations.
As a caveat, Oracle (the owner of all Java trademarks) has given third parties leave to use the Java trademark (and a few others) in very specific ways for their products. In general, for products that will interface somehow with Java, to make this situation visible (and thus, the "for Java" allowance) if, and only if, you make it very explicit that your product is not a part of Java, only related to it peripherally.
Even then, you're not allowed to trademark a name with Java in it. You must trademark a name without the Java brand, then you can add the "for Java" (or equivalent) every time you use your brand.
Another requirement to use Java in that way is that, when represented graphically, it must appear as subscript to your brand name, and it cannot use the colors most attributed to the Java brand (or Oracle), so no red for Oracle, no Orange+Blue/Grey for Java, etc.
The legal docs for this are very specific and clear on the issue. I cannot fathom how anybody can keep arguing this issue, unless they're doing it deliberately (like the Java Guardians, whose position on this is that they wish Oracle would extend a more permissive licence on the brand to us, but they perfectly acknowledge this is a legal issue over Oracle owned brands).