Imagine your name was human

Luna ..

Moon (with capital M) is the actual name though, and isn't it cool having an entire species named after you?

I guess we'd finally understand how every single one of Ash's Pokemon feel

One way to think about it is that in all the countries/empires/cultures that these names originate in if they could see the other planets and moons in as much detail as we can they would describe them object class wise as "like the sun" or "like the moon." You have to remember a lot of this comes from the people that would name a set of twins "Augustus" and "not Augustus."

That's because you are The Moon and the others are a moon.

But that's like the Moon-moon.
So we have MoonMoon the dog and MoonMoon the celestial object.

but you're like the OG.