Trademarks are a business thing, so a personal name isn't a trademark unless that person uses it as such in a business or similar enterprise. Such things as Microsoft Windows and ASP.NET are trademarks. I could trademark "David Thornley" software if I were to write and distribute it (remember Peter Norton and the Norton Utilities?), but since I'm not actually in that business my name isn't a trademark.
Also, pay attention to the wording. The license doesn't grant any rights to a trademark, but it doesn't restrict any ability you already have. You can't call your project Microsoft software, but you can advertise that it runs on Microsoft Windows. The guiding rule (at least in the US) is if you're trying to create any confusion about who produces the software, or if a reasonable person could be confused. You'd probably be safe calling it "Project Gligoran, using ASP.NET and running on Microsoft Windows", but if you're worried consult a trademark lawyer.
Also, in the US, trademarks work on a "protect it or lose it" basis. If you use a trademark improperly, and the owner of the trademark finds out about it, the owner is legally required to take some sort of action against you or risk losing the trademark.