Many people have been wondering what is with Boruto's eye and whether or not it is an evolution of the Byakugan. the answer is yes, yes it it.
But to explain what is going on, we have to explain some history of the Naruto verse and Boruto's lineage.
As most people reading this probably already know, the original Hyuga ancestor was Hamura Ootosuki, the brother of Hagoromo Ootosuki (Sage of Six Paths). After Hagoromo and Hamura sealed their mother Kaguya, Hamura went to the Moon to watch over the Juubi husk. This sets up the events for Naruto the Last.
Now comes the focus of the articles and the key plot point of Naruto the Last, the Tenseigan. It is the Byakugan equivalent to how the Sharingan eventually evolves into the Rinnegan (which is another topic for another day). Just like Rinnegan, achieving the Tenseigan is an incredibly complicated process that requires a hundred different things to go right. Let's go through everything the has to go right for the Tenseigan to activate:
Boruto does not have have the Tenseigan, but a variant of Hamura's Byakugan
Hinata never had the Tenseigan, but she does have Hamura's chakra. Also being Naruto's son, he has various benefits of Uzamaki, Sage, and Kyuubi chakra. Too sum up the extra benefits:
So overall what is Boruto's doujutsu?
It is a brand new type of doujutsu that is the result of Hinata's Hamura chakra and Naruto's Uzamaki, Kyuubi, and Hagoromo chakra.