One of the more salient points undergirding pitches for collective action on things like climate change is that we share this place we call Earth, not only with our contemporaries but with future generations. Both states and individuals can claim ownership of some portion of land or sea or sky, but true ownership ultimately eludes any such as us who are transitory figures on a body that has existed long before we arrive and will continue to exist after we've departed as a species.
No such existential considerations impinge upon intellectual property, it would seem, as a fight over the ownership of the word "planet" is taking place in France. Per the Associated Press, Planete Amazone and Run for Planet - 15 Million Trees, both French environmental groups, have received pushback over their use of "planet" (or "planete" in French) in any material or, in the case of Planete Amazone, their attempt to trademark the company name.
The resistance comes from French entertainment company Canal Plus, which holds a trademark on the term in France. This clearly presents an issue for environmental groups whose efforts are focused on that very same planet, and who would be hard pressed to work around that trademark. ("World" isn't necessary evocative of the environment, and "globe" suggests something many of us had on our desks in grade school.) To that end, Planete Amazone, Run for Planet and other environmental groups have taken their case to the French National Intellectual Property Institute (INPI) in an attempt to gain permission to use the term, with Planete Amazone also negotiating with Canal Plus over the right to use "planete".
The AP article has further reporting on the letters received by the named environmental groups from Canal Plus, with the studio presenting past rulings from the INPI in its favor as well as the case for its strong "planete" brand in the European market. And while all of what Canal Plus alleges may be true, it doesn't address the larger question of whether the practice of trademarking terms like "planet" is right or good, in any country. Branding and trademarks are separate from language itself as it's used by people, certainly, but it nevertheless seems hard to imagine how any company could claim exclusivity over the term, no matter how prevalent it is in their marketing. "Planet" itself is such a global term (no pun intended) that it's hard to see from the outside how it could ever gain the specificity needed for a trademark, but again, we run into questions of language versus intellectual property law.
It's also important to remember that the law isn't a morality tale, but you can nevertheless hope that groups that are doing the work to try and preserve the planet are able to use the mark rather than having it remain exclusively in the domain of purely capitalist branding, but the latter result would be more in line with how things tend to actually go, so it's probably a mistake to hold your breath.