His alias 'Ryuuzaki' comes from a killer that he and Naomi Misora caught together a couple of years before the start of the Kira investigation. 'Rue Ryuuzaki' was an alias that Beyond Birthday used.
Here is what Wikipedia says about Beyond Birthday's character:
Beyond Birthday (ビヨンド・バースデイ, Biyondo Bāsudei?) or BB, a character exclusive to the Death Note prequel novel, "Death Note Another Note: The Los Angeles BB Murder Cases", is a crazed serial murderer bent on surpassing L - not sa pamamagitan ng being the world's greatest detective, but sa pamamagitan ng being the world's greatest criminal. The novel, a prequel to the manga series, takes place in August 2002, over a taon before Light became Kira. The only thing known about his past before going to Wammy's House is that his father was beaten to death sa pamamagitan ng a thug and his mother died in a train crash. Like L, Mello, Matt and Near, he lived in Wammy's House and was known as B, which stood for "Backup." A, the original successor to L,[clarification needed] had killed himself years earlier due to the pressure of living up to L. Birthday was born with Shinigami eyes, so he could see when humans would die, and their names. Using his shinigami eyes, he would intentionally kill people on their destined araw of death.
To fool Naomi Misora, he acted a bit strange during Naomi and L's investigation, calling himself Rue Ryuzaki (竜崎 ルエ, Ryūzaki Rue?), with "Rue" being an anagram of the Japanese pronunciation of L (エル Eru), and Ryuzaki being a nickname L later adopts. He was always in heavy makeup when with Naomi, so his true appearance is unknown. He killed 3 victims, Backyard Bottomslash, Quarter Queen, and Believe Bridesmaid, while leaving clues at each murder scene for Naomi Misora to "solve." In reality, he himself led her to each conclusion she made.
He attempted to commit suicide at the end of the novel, sa pamamagitan ng setting himself on fire, to look like the final victim. He felt that L would never be able to solve the case if he, the murderer, were "murdered", meaning he would have outwitted L. Naomi Misora, however, figured out his plan at the last moment, saving Beyond Birthday's life while at the same time putting him under arrest for his murders. At the very end of the novel, the narrator, Mello, states that Beyond Birthday died of a mysterious puso attack several years later in prison. According to Death Note How to Read 13, he was killed sa pamamagitan ng Kira and the Death Note.