While it has been some time since Kawaki obtained Isshiki Otsutsuki's dojutsu in the Boruto manga, the eye's name has yet to be revealed. However, a recent fan theory has decoded its name through a theory based on the events that took place in the first chapter of the Two Blue Vortex manga.
While Kawaki was Isshiki's vessel for quite a long time, he only got to manifest the Otsutsuki's dojutsu after Isshiki's soul passed away. Since then, Kawaki has used Isshiki's dojutsu on multiple occasions. With that, he was able to use the two Otsutsuki techniques - Sukunahikona and Daikokuten.
Disclaimer: This article contains spoilers from Boruto: Two Blue Vortex.
Boruto: Two Blue Vortex may have hinted at the name for Kawaki's dojutsu
According to a theory by a Boruto fan on X (formerly Twitter) @momosrighthorn, Mitsuki may have hinted at the name for Kawaki's dojutsu.
As fans would know, manga creator Masashi Kishimoto loves connecting the lore behind his series to dharmic religions. That's why he must have designed the dojutsu's shape similar to the wheel of dharma.
The only difference between the wheel of dharma and Kawaki's dojutsu is the inversion of colors, but that might have been an artistic choice to make the dojutsu stand out.
The dojutsu does not always look the same. Its center, which is a radiant yellow pupil, lights up like a sun when it gets activated.
With that, the sun-like pupil forms the hub of the wheel of dharma. Normally, symbols like the wheel of dharma are associated with the sun, so it can be theorized that the pupil was made to resemble a sun
However, there might have also been a plot reason why the pupil looks like the sun. When Mitsuki was first introduced in the manga, Orochimaru helped him find his "sun" by directing him to Boruto.
However, except for the fact that Mitsuki's name partly meant "moon," there was no need for him to address the Hokage's son as his "sun."
Following Boruto and Kawaki's switch at the end of Boruto: Naruto Next Generations manga, the entire idea behind "sun" and "moon" may have finally gotten exposed.
Following the switch, Kawaki had become Mitsuki's "sun." Nevertheless, Boruto: Two Blue Vortex chapter 1 saw Mitsuki wondering whether Kawaki was actually his "sun."
"You're the sun...shining brightly upon my moon...aren't you...Kawaki?"
Momosrighthorn theorized that Kawaki currently being Mitsuki's "sun" was planned from the get-go. Masashi Kishimoto may have wanted to connect Kawaki's dojutsu to Mitsuki's perception of him.
Therefore, momosrighthorn believed that Kawaki's dojutsu name might be in some way a derivative of the wheel of dharma. While the fanbase has begun calling Kawaki's dojutsu "Dharmagan," the name wasn't localized for the Japanese.
Hence, the fan believed that the plausible name of Kawaki's dojutsu might be "Horingan." "Ho" (法) meant Dharma, "Rin" (輪) meant Wheel, and "Gan" (眼) meant Eye. While the manga is yet to confirm the dojutsu's name, with this theory, the fan may have come close to deducing the same.