Lunar's alternate form/disguise
The reason why he created a disguise is because other aliens kept harassing him.
In the future, the knowledge of Lunar's existence will spread across the universe. "A New Astral have been discovered."
Many aliens will come long and far to find Lunar. Many who are Followers of Astrals in general. All looking for Lunar to grant them their "Wishes".
Many don't know/refuse to acknowledge that Lunar is NOT a legitimate Astral. Lunar can't exactly grant "Wishes" like other Astrals, either.
After many, many, many attempts to deny these aliens and to leave him alone, Lunar had enough.
A lot of these aliens do not understand the concept of no. Some even think they can just take advantage of Lunar just because he is consider a weak Astral, aka a "Fragile Star"
So Lunar tries a new method these Followers would understand.
Violence, aka acting like an Astral.
Astral in general a territorial and violent beings, so Lunar decide to act like one. Putting on a disguise to make it more clear on the connection with the fellow Astrals and to put on a show.
Many of these Astral Followers know better then to be around an Astral when they are actively irritated. So many will stay away out of fear.
Lunar doesn't want to be the bad guy but it was getting to a point that these followers were becoming violent themselves. And Lunar didn't want anyone else getting hurt/die because of him.
His disguise takes a lot of energy out of him. Unlike his lighting attack that only require harnessing star energy for a split second, this disguise required him to cover his entire body with consistent flow of star energy. This is extremely taxing while also needing to still perform his basic moves, like lighting and flying. This results in his disguise only lasting for 10 to 20 minutes before he overheats to dangerous levels and shuts down to prevent any further internal damage. Lunar isn't overly worried by that fact because he knows he has Gemini to catch him if he shuts down.
Gemini will be aware of this whole situation. Even offering to "get rid" of these followers for good for Lunar but he didn't want them to do that. To not repeat last time.
So he would asked Gemini to let him handle it. Gemini would agree to this. They trust Lunar.
Gemini even shows support on his idea of a disguise by placing their own crescent ornament on top of his head as a final touch. To represent their support on his idea and trust that he knows what he is doing.
It's to also show claim in a minimal way. Only few of the Astral Followers are aware who that crescent moon belongs to. The followers will get the hint that they are not just angering one Astral, they are angering two.
(BTW All the other Astrals do think it's adorable/funny that Lunar is trying to look and act like them.)