Family
Senku Ishigami
Byakuya and Senku
Senku is Byakuya's adopted son. Senku was the son of Byakuya's good friend. Byakuya supported Senku's research and once sold his car to fund it. He and Senku shared many traits, including a love of science, exploration, and a limitless respect for human ingenuity and creativity. More than this, though, Senku inherited an even more important trait from his father: A belief in the importance of fun and its critical role in helping humanity to survive. This ability to find joy in anything from research to tasks as nerve wracking as saving lives was what allowed both men to withstand all of the hurdles they came across. Byakuya deeply loved his son, though humbly credited Senku's genius as being all his own, as they were not biologically related. This was the only reason that Byakuya ever brought up that he was not Senku's birth father, as he loved Senku as his own, doing whatever he could to support him.
Byakuya's faith in his son was demonstrated in making Senku the subject of the last story of The Hundred Tales, believing that his son would eventually come across Ishigami Village and wanted his descendants to be prepared with the knowledge of his son. He left coded messages in The Hundred Tales for Senku to uncover, including a time capsule containing a glass record of Byakuya's final message to Senku as well as music that was included, fulfilling his desire for Lillian to sing for his son. He left the song there as a gift to humanity to bring them together. At the time of his death, his last thoughts were of his son, showing that his belief was maintained even after decades.
Friends
Connie Lee
Byakuya was friends and colleagues with Connie during their time aboard the ISS and their time together after the Petrification event. He celebrated her and Shamil's wedding, having officiated the event himself. After her and Shamil's deaths, he and Lillian assumed the role of adoptive parents to their children.
Lillian Weinberg
The singing star and professor formed a fast friendship and bond aboard the ISS. There, they played a practical joke on Darya and Yakov, trying to convince them that Lillian was an insufferable diva, only for Byakuya to break character and give away their act. Byakuya was enamored by her talent and asked her if she would someday sing for Senku. Lillian happily agreed to his request. After the Petrification, Lillian and Byakuya bonded further during their time on the island together. Lillian, at some point, confided her despair that all of humanity's music would be lost as a result of the Petrification, with Byakuya comforting her and reassuring her that it wouldn't all be for naught.
He eventually thought to create a record that included a message to Senku along with a song performed by Lillian, Yakov and Shamil on vocals, guitar and drums, respectively. This was done by them as a gift to Senku and their descendants.
Eventually, as their friends died of pneumonia or were lost at sea, Lillian and Byakuya became the adoptive parents and caretakers of their friends' children. Sadly, Lillian would also succumb to the illness, leaving Byakuya heartbroken and the last of the Soyuz team.
While it is not confirmed, it is strongly implied through the resemblance of the villagers of Ishigami Village that Byakuya and Lillian eventually married and had children of their own.
Darya Nikitina
The two were colleagues on the ISS and got along well. Eventually, they returned to Earth together and founded Ishigami village. He became the custodian of her and Yakov's children when they were lost at sea in an attempt to find antibiotics on the mainland.
Yakov Nikitin
Like his wife, Yakov got along well with Byakuya, making friends with the eccentric Japanese professor. His children were left in Byakuya's care after he and Darya were lost at sea. Yakov was kind and very earnest in his desire to assist in Byakuya's endeavors.
Shamil Volkov
The Russian lone wolf did not initally get along well with Byakuya's mercurial personality, remaining stoic and practical to a fault. He attempted to dissuade Byakuya from attempting to return to Earth alone, going so far as to punch him in the stomach to prevent Byakuya's impulsiveness from potentially dooming them all. Shamil eventually softened during their time surviving on Earth, becoming friends despite his retention of his stoic personality. The two came to a final understanding upon Shamil's death from pneumonia, as Shamil confessed that despite the apocalyptic circumstances, that thanks to Byakuya, he had fun, fell in love, and even had children that he never dreamed of. Thanks to Byakuya, he died happy.
Dr. Xeno
Xeno was Senku's co-worker at NASA's american branch and Senku's mentor. They cross paths a few times back in the Pre-Petrification World.