Kenshin retains the name throughout the Rurouni Kenshin OVAs and the original series. It is a name which strikes fear into the hearts of his enemies.
In the original series, Kenshin suffers from split personality disorder, one side is the humble wanderer Kenshin and the other is the Hitokiri Battousai Kenshin. This is sometimes referred to as 'transforming into the Battousai', a prospect which frightens Kenshin and his friends immensely.
Shinsengumi Soldier 2: It's the Hitokiri Battousai!