In history

We're commonly know, other then the Hakuouki one, the Hajime Saito from Ruronin Kenshin. But the truth is that Hajime Saito is an historical character of great importance who lived in the Edo Period. As Kenshin and Hakuouki described him, he was the captain of the shinsengumi's third division.

Here a brief description from wikipedia.

"Saito was born in Edo, Musashi Province (now Tokyo). Very little is known about his early life. He was born Yamaguchi Hajime (山口一) to Yamaguchi Yuusuke (山口祐助), an ashigaru of the Akashi Domain, who had bought the rank of gokenin (a low-ranking retainer directly serving the Tokugawa shogun). He had an older brother named Hiroaki and an older sister named Katsu. According to the published records of his family, Saito left Edo in 1862, after accidentally killing a hatamoto. He went to Kyoto and taught in the doujou of a man named Yoshida, who had relied on Saito's father Yuusuke in the past. His style comes apparently from Itto-ryuu or Mugai Ryuu."