Silent Night, Deadly Night

In 1971, 5-year-old Billy Chapman and his family went to a nursing home to visit his catatonic grandfather. When the family steps out of the room and leaves Billy alone with his grandfather, the old man suddenly springs to life and warns him that Santa Claus punishes the naughty. That night Billy's family happens to come across a man dressed in a Santa Claus outfit seemingly having car trouble. The man who is actually a criminal who just uses the disguise to commit a robbery in a liquor store, in which he killed the clerk. He then kills Billy's father with a handgun and slits Billy's mother's throat with a switchblade in front of him and his crying infant brother Ricky. Billy then runs off to hide, leaving his baby brother in the car. However, the murderous Santa leaves the children alive. Three years later, Billy and Ricky are celebrating Christmas in an orphanage run by Mother Superior, a strict disciplinarian who persistently strikes children who misbehaves and considers punishment for their wicked actions a good thing. Sister Margaret seems to be the only one who sympathizes with the children. She tries to help Billy open up and play with the other children, but Billy is constantly subject to Mother Superior's scrutinizing eyes and regularly punished. On Christmas morning, the orphanage has a man in a Santa Claus suit who visits the children. Because of Billy's childhood experience, he's terrified. Mother Superior drags Billy kicking and screaming to Santa, where he punches him in the face, causing his nose to bleed and flees to his room with amid looks of horror.
Ten years later, 18-year-old Billy leaves the orphanage in hopes of finding a normal life. He obtains a job as a stock boy at a local toy store and develops a crush on his coworker Pamela. Billy's sexual thoughts regarding Pamela are often interrupted by morbid visions of his parents' murderer. However, he steadily grows unstable.
On Christmas Eve, despite his protestations, Billy is coerced by his jeering coworkers into dressing him up as Santa Claus for the store. Shortly after the store closes and the store staff party begins, Billy happens upon Pamela almost being raped by another coworker, Andy. Billy snaps, finally insane he hangs Andy with a string of Christmas lights and kills Pamela with a utility knife, uttering darkly that punishment is good. Billy's boss, Mr. Sims happens upon the scene where Billy kills him with a hammer. Mrs. Randall discovers Billy's grisly work and attempts to flee, but is attacked with an axe then killed with an arrow in her torso.
As his rampage continues, Sister Margaret comes in only to discover the carnage and returns to the orphanage to seek help via telephone. Billy breaks into a nearby house to attack the two young couple: Denise and Tommy, who were seemingly having sex. After he hacks the door down with a double-bit axe, he impales Denise on a set of deer antlers before he throws Tommy through a window to his death. Denise's little sister Cindy (who was told to get in bed before) interrupts Billy. Rather than attack her, Billy simply inquiries whether she's been naughty or nice. He smiles warmly and "gifts" her a bloody knife he used earlier. Billy exits and witnesses bullies picking on two sledding teenage boys. Suddenly he appears and decapitates one of the bullies, caused the other one to flee in horror. Meanwhile, the authorities are investigating the ongoing murders with the aid of Sister Margaret, who has deduced that Billy is the killer and postulates that he is making his way back to the orphanage.
The next morning, a man dressed in a Santa Claus outfit approaches the orphanage. Officer Barnes warns the man to stop but he does not and Barnes shoots him. To his horror, Barnes discovers that the man was in fact Father O'Brien, a deaf pastor on his way to the orphanage when a call came through from a police radio scanner. Billy appears and kills the distraught Barnes with the double-bit axe as punishment and hacks off the head of the snowman with the sudden bloody axe. Billy arrives at the orphanage, through the use of his Santa costume and gains entry and Mother Superior, now in a wheelchair who disbelieves in Santa Claus. Billy raises the axe, yells "Die" and prepares to kill her but is interrupted by Captain Richards' who shoots him. Billy is then struck in the back and collapses. He looks at the nearby children and utters "You're safe now, Santa Claus is gone" before succumbing to his wounds. As the children gather around, an attending Ricky coldly stares at Mother Superior before he eerily utters "Naughty".

Question: What is Billy's brother's name?
Answer: Ricky