Oda Nobunaga ordered Hideyasu's older brother, Nobuyasu, to commit suicide in 1579. Thus, Hideyasu would have been poised to inherit the head of the Tokugawa household. However, as part of a peace accord between Tokugawa Ieyasu and Hashiba (Toyotomi) Hideyoshi, he was forced from his home and adopted by Hideyoshi. Thus, he is known to have adopted the name "Hashiba Hideyasu," taking the "Hide" from "Hideyoshi" and the "yasu" from "Ieyasu."
He would later be adopted into the Yuuki family. It was common for a man to be adopted into a family for an arranged marriage. Thus, his name changed again, and he is now known as Yuuki Hideyasu.
After the Battle at Sekigahara, he was made the first lord of the Kita-no-Shou Han, now part of the Fukui Ken. He died in 1607, presumably from being poisoned.
In the game, Hideyasu dies at the time of the Battle at Sekigahara. Miyamoto Musashi 宮本武蔵 and Majima Gorohachi 真島五六八 are enlisted by Marume Nagayoshi 丸目長恵 to assassinate him in a secret plot designed by Nankoubou Tenkai 南光坊天海, a monk and chief advisor to Tokugawa Ieyasu. Because Hideyasu is Ieyasu's son and heir, even though he apparently was at odds with Ieyasu, he could not kill him directly. So, Tenkai decided to send troops to kill Hideyasu, and then kill those troops to avenge the death of the heir to his lord.
This is a common strategy. This way, you could assassinate someone, and then make it look like you were defending them by bringing their murderers to justice.
In his final moments, Hideyasu tells Musashi he regrets that he was unable to keep his younger brother from Tenkai's clutches."