Backstory
The novel (and Godfather Part II) explains that Vito was born in the small Sicilian town of Corleone in 1887. The film implies the date of birth 6 June 1887, though the tombstone seen in The Godfather 
shows an earlier date, and the reference to Pearl Harbor made in The Godfather Part II could indicate Vito's date of birth to be December 7th. His father, Antonio Andolini, is murdered by the local Mafia boss, Don Ciccio, because he refused to pay tribute to him. His older brother, Paolo, swears revenge, but is himself murdered soon after. Eventually, Ciccio's henchmen come to the residence of the Andolinis to take Vito away and have him killed. Desperate, Signora Andolini takes her son to see the mafia chieftain herself.
When Vito's mother goes to see Don Ciccio, she begs him to spare Vito. However, Ciccio refuses, reasoning that Vito would also seek revenge as an adult. Upon Ciccio's refusal, Signora Andolini puts a knife to his throat, allowing her son to escape, but is then shot dead by Ciccio's guards. (In the novel, she survives being shot and later reunites with her son in Sicily many years later.) Later that night, he is smuggled away, fleeing Sicily to seek refuge in America on a cargo ship full of immigrants. In the novel, he deliberately changes his name to Corleone, after his home town. The film, however, plays that he is renamed "Vito Corleone" because the immigration workers at Ellis Island mistake "Andolini" for his middle name and the name of his town for his last name. According to The Godfather Part II, he later adopts the middle name "Andolini" to acknowledge his heritage.
