Kodi is open source and copyrighted using the GPL. Basically, this means that anyone can download and use the software, and modify it for their own use. A lot of folks do this all the time, even me in my own small way. Some of those uses aren't entirely legal, mostly by using pirated sources for video streams. In itself, that's not a major issue for Kodi - those people are doing something illegal, but Kodi is just one of the tools that they're using. In the same way that it's not the fault of the car when the driver breaks the speed limit, the Kodi software isn't at fault with people use it to pirate media.
The problem that the Kodi developers have is that some unscrupulous folks are spreading their illegally modified software around, and using the Kodi name to do it. Some of these people sell some kind of cheap hardware with a modified version of Kodi pre-installed, advertising something along the lines of "Kodi lets you watch free TV and movies." Others use Kodi in videos that show people how to install Kodi add-ons that access pirate sites.
This means two things that are bad for Kodi: the customers come complaining to Kodi (not the original seller) when things stop working, and the world views Kodi as a source of pirated media. The former causes a whole lot of wasted time and effort by the Kodi developers. The latter makes it near impossible for Kodi to do legitimate business.
So the Kodi developers are trademarking the Kodi name and logo, and will be going after those using their name without permission by issuing takedown notices and possibly other legal action. People may still be doing the same things with the software, but they'll have to stop using the Kodi name to do it, or face legal consequences.
I support the Kodi developers on this, but I'm not sure how much it's going to help. Protecting the use of their own name makes sense, and I certainly hope they can stop the worst of the abuses. However, the public perception of the media platform as a support for piracy isn't likely to go away. No matter what name is used, the software is still open source and extensible, and people are going to write code that puts it to illegal use.
It might help if Kodi can find a way to push a positive image, as well as attacking the negative image problem. Kodi can be used for legitimate purposes, and there's a lot of potential currently untapped. There aren't Kodi add-ons for many of the most popular media services, and those that exist are unofficial and break often. (Even the Crunchyroll add-on that I use is unofficial, and that's a pretty minor service.) If Kodi had stable, supported connections to useful services that people want to use, I think that would go a long way toward changing perceptions from "Kodi is a pirating platform" to "Kodi is a legitimate media platform."
In any event, I wish the Kodi team the best with their efforts to change public perceptions of their project, and keep control of how their name is used. As well as good luck getting out from under whatever DDOS attack or hack is causing problems on their site.
