In The Hairy Ape, what was Yank's childhood like?

Yank does not give many specific details of his life as a child, but from what we can gather, it seems particularly brutal. Yank grew up relatively poor and had a miserable home life situation. His father was physically abusive and beat him relentlessly. His mother died of the "tremens," which is a severe state of cardiac irregularity and delirium brought on by alcohol withdrawal. This condition only occurs in a small percent of people suffering from the most severe alcoholism, so it is not a stretch to assume that Yank's mother was a severe, non-functional alcoholic.

It is said that on Saturday nights in particular, Yank's parents fought so violently and relentlessly that they would break parts of the house. He denies that this had a negative affect on him, saying he's a "chip off the old block" and is tougher for the abuse. However, whether he admits it or not, this haunts Yank for the rest of his life. It is his mother's death that galvanizes Yank to leave home and change his circumstances.

It is perhaps this childhood that dooms Yank to a life of feeling as though he does not belong. He is far too unintelligent to make his way in the world by himself, and when he is told that he doesn't belong as a stoker, he loses the one piece of the world where he truly felt at home.

Annoyed at the men singing a song about a girl waiting at home for them at the beginning of scene one, Yank says the ship is his home. What they are calling home was the place he ran away from when he was a kid. "Home was lickings for me, dat's all." Meaning that all he remembers from home was his parents beating him.

The other men shout Yank down for saying the ship is his home because for them the ship feels like hell. However, for Yank to feel so comfortable in such poor conditions shows just how bad Yank's home life must have been.

We get further insight into Yank's childhood in scene 5 when he tells his friend Long that his parents used to leave him at church while they went home to get drunk:

Dey never went demselves, dough. Always got too big a head oon Sunday mornin', dat was dem.

Once they were drunk, they would fight so hard that it was like watching two professional boxers:

Dey was scrappers for fair, bot' of dem. On Satiday nights when dey bot' got a skinful dey could put a bout oughter been stages at de Garden.

Yank ran away soon after his Mum died of alcoholism.

In the first scene, Yank gives the impression that he feels sad about his upbringing and the person it has made him into. However, the more people challenge him about who he is—in particular, after Mildred calls him an ape, the more defensive he becomes. In scene five, he proudly states that his parents taught him how to cope with punishment:

I'm a chip offen de old block, get me?

Yank is undereducated; his own personal philosophies about "belonging" and his role in society are his only real driving force. Yank's lack of education is likely due to his childhood, which is only mentioned in passing; Yank speaks of running away from home while still a child to avoid "lickings," or beatings for disobedience. This was considered acceptable in the early 20th century, but since Yank removed himself from discipline, he had no motivation to learn or strive for higher education. Instead, he grew up "street smart," with his views clouded by a superiority complex based on physical strength.

"T'hell wit home! Where d'yuh get dat tripe? Dis is home, see? What d'yuh want wit home? (Proudly.) I runned away from mine when I was a kid. On'y too glad to beat it, dat was me. Home was lickings for me, dat's all. But yuh can bet your shoit noone ain't never licked me since! Wanter try it, any of youse? Huh! I guess not."
(O'Neill, The Hairy Ape, eoneill.com)

Yank's refusal to learn is based in his unstructured youth; without respect for authority, Yank probably dug in his heels whenever personal improvement was mentioned. His childhood also would have been focused on personal survival rather than learning, because he had no family to support him; his respect for strength would draw from his own experiences overcoming enemies. Yank's childhood was probably harsh and difficult, and his anger at the world is based in that adversity.

In The Hairy Ape by Eugene O’Neill, why is the character called Yank?

In The Hairy Ape by Eugene O’Neill, Robert Smith is normally referred to as "Yank" despite its not being his real name. It is what is known as a "nickname", a name given to someone informally within a small group, sometimes as a form of affection. The use of nicknames often increases group cohesion and solidarity, functioning in anthropological terms as a new identity refecting initiation into group membership. The name "Paddy," also a nickname, reflects Irish ancestry, and "Yank" is a common British term for Americans, and thus "Yank" defines its possessor as prototypically American.

His initial "can do" attitude and dialect are meant to evoke almost a cliche of the American (the Yank or Yankee) as seen by other nations, as scene in this speech:

Yank: "What's dem slobs in de foist cabin got to do wit us? We're better men dan dey are, ain't we? Sure! One of us guys could clean up de whole mob wit one mit. Put one of 'em down here for one watch in de stokehole, what'd happen? Dey'd carry him off on a stretcher. Dem boids don't amount to nothin'. Dey're just baggage."