You can own whatever you want of the moon. I own a Galaxy. Just grabbed one last week when we found out there are trillions of them out there.

Phonetically my galaxy is now called "Tibadon".

With at least a billion solar systems, I certainly have lots of sentient beings that are going to need my help with their planets, sooner or later. Here is my official claim document. A tweet is sufficient.

https://twitter.com/BobThibadeau/status/1546675090074517504?s=20&t=9QG_k7scC60OKctSlfSbVg

If you didn't know it, the way a new Species is named is that you publish in one of about four journals a paragraph that names it with the linnaean name you just made up, whether animal or vegetable. So, most certainly, a Twitter claim for a galaxy has to be as good as that, right? There's plenty of them to go around as long as we all agree each of us can only own one. I also propose that unlike the British practice, a Company cannot own a galaxy. That would be wrong. (And yes, I already got a star for my birthday once, but it is iffy if it has any sentient beings or even any planets.)