of Atticus. They are not equal to their father, and they know it well. Their father, in fact, has significant authority over his children. Yet he rarely exercises it. He prefers to teach them through open discussion and questions and answers. He wants them to obey but also to understand why they must obey. Scout and Jem respect him greatly for this, for they recognize that he makes them think critically. By calling him “Atticus,” they combine respect with this recognition that they are called to grow in maturity and knowledge.

Further, the children's use of their father's first name suggests intimacy. They don't call him “Mr. Atticus” as they would if they were referring to another adult. They drop the “Mr.” out of intimacy. Scout and Jem clearly love their father very much. He is not just any “dad” or “papa” to them. They love him for who he is as a person, for they know him well thanks to his encouragement of deep discussions even about difficult subjects. They can come to him with any issue, and he will treat it with respect and seriousness. He also deals with each of his children as an individual with his or her own personality and needs, and they, in turn, recognize their father for the unique individual he is.

It's not reasonable to think that Jem and Scout called Atticus by his given name because of an equality issue. In the South, at the time this amazing novel is set, equality wasn't possible between child and parent any more than equality was possible between black and white. That is the answer in my opinion. Atticus defended Tom Robinson, not because he thought there was a slim possibility he would exact justice on behalf of Tom, but because it was the right thing to do. It wasn't popular. It wasn't endorsed by the current culture, but Atticus couldn't do otherwise. Instinctively, his children knew this about him, and although the current climate forbade them to call him his given name, they did, because, quite simply Atticus was too real, too large, too important, to be called anything other than he was.

This writing device was a symbolic way of honoring what was right, real, raw, and true, despite prejudice and social norm. It parallels the trial in the novel and Harper Lee displayed genius.

Scout does call Atticus "my father" when she is recounting her childhood experiences from an adult perspective.  However, as a child, both she and her brother indeed did call him Atticus. 

To understand how radical this was, one must understand a bit a bit about Southern culture, where, to this day, many children would never dream of calling their parents by their first names, and often that Miss, Mrs, or Mr, is followed by "ma'am" or "sir."

There are several theories about why Scout and Jem were permitted this familiarity.  One suggestion is that this lack of manners is indictive of Atticus' poor parenting.  The children grow up without a mother, raised largely by the maid Calpurnia instead.   Atticus is so busy with his law practice and distracted that he never bothers to teach the children proper social rules.

Another take is related to Atticus' own beliefs in the power of children and the unearned respect adults are often given.  The children call Atticus by his first name in order to cultivate a more open, rather than authoritarian, relationship.  Atticus wants to keep the pathways of communication open between himself and his children.  Allowing them to call him by name is a way he keeps their relationship more level. 

There are certainly many theories as to why Scout and Jem address their father as Atticus. Perhaps Atticus wants his children to see him as someone they can trust and depend on when the chips are down; if we look at the text, we see this desire clearly in the way Atticus communicates important life lessons to his children. Atticus' patience is only exceeded by his steadfast adherence to honorable conduct; while he never laughs at childish ignorance and never minces words when a situation calls for it, he does not tolerate unprincipled behavior from Scout and Jem. He is able to engage his children while maintaining clear evidence of his love for them in their communications.

His style of parenting is such that he actually takes the time to reason with and to talk with his children as if they possess both the emotional and mental intelligence to comprehend the rationale behind his actions. He treats his children with great respect; I would say that this great belief in egalitarianism  is probably the main reason why he allows his children to address him as Atticus. He never belittles Scout and Jem's intelligence by exhibiting indifference, apathy, or disgust towards their immaturity. To Atticus, his children are human beings worthy of the same consideration and respect adults deserve. Both Scout and Jem can trust that Atticus is always going to be honest with them and that, no matter what happens, they can trust him to be fair.

Take for instance the situation when Jem cuts down every single one of Mrs. Dubose' camellia buds. Jem does this because of his loyalty to his father. Mrs. Dubose's ugly accusation of Atticus lawing 'for niggers and trash' is more than Jem can stand. Let's look at how Atticus deals with it:

“Son, I have no doubt that you’ve been annoyed by your contemporaries about me lawing for niggers, as you say, but to do something like this to a sick old lady is inexcusable. I strongly advise you to go down and have a talk with Mrs. Dubose,” said Atticus. “Come straight home afterward."

Notice that Atticus doesn't yell at Jem or attempt to humiliate Jem through condemnation. He does not resort to guilting Jem into remorse, either. He first starts out by expressing his understanding of Jem's actions and then proceeds to clearly state why Jem's behavior is wrong. Then, he tells Jem exactly what he needs to do to address his own actions. Atticus basically treats Jem the same way he treats the despicable Bob Ewell and the hapless Mayella in court. Atticus never neglects the facts, but his delivery is always dignified, principled, and steady, even when it has to be strongly worded.

When Scout accuses Atticus of betraying Jem, Atticus answers:

“Scout,” said Atticus, “when summer comes you’ll have to keep your head about far worse things... it’s not fair for you and Jem, I know that, but sometimes we have to make the best of things, and the way we conduct ourselves when the chips are down—well, all I can say is, when you and Jem are grown, maybe you’ll look back on this with some compassion and some feeling that I didn’t let you down. This case, Tom Robinson’s case, is something that goes to the essence of a man’s conscience—Scout, I couldn’t go to church and worship God if I didn’t try to help that man.”

Atticus' response to Scout acknowledges her concerns but also highlights the truth of what the children will face when the whole town realizes that their father will not back down from his principles. Atticus' authenticity and transparency in discourse is fully demonstrated in the implications of his children's address to him.

To Jem and Scout, the name 'Atticus' means truth, friendship, respect, trust, and honor. It is the name for 'father' and 'friend.' Atticus is willing to flout the conventions of Southern norms of respect in order to unequivocally demonstrate his love for his children. He strikes me as someone who also exhibits great compassion for the limits of one's humanity. When Jem admits that he isn't really sorry despite his apology to Mrs. Dubose, Atticus responds:

“There was no point in saying you were sorry if you aren’t,” said Atticus.

So, you can see that everything Atticus stands for is demonstrated in his daily interactions with his children and his neighbors. In allowing his children to address him by his first name, he acknowledges both his humanity (and theirs) and the principles by which he has chosen to live by and to raise his children with.

This is a fantastic question. The interesting thing about this question is that the book never really addresses why the children call their father Atticus instead of "dad" or "father." In light of this, we can only guess.

First, it should be noted that when Scout reflects upon her past, she does call Atticus father. Here is an example: 

"Jem and I found our father satisfactory: he played with us, read to us, and treated us with courteous detachment." 

Second, some might say that this practice was owing to the death of their mother. In other words, when Jem and Scout's mother passed away, Atticus was not able to raise his children well. Aunt Alexandra seems to suggest this. For example, she wanted to educate Scout in proper manners. 

Third, another thought is that Atticus wanted his children to call him Atticus. I prefer this interpretation, because there does not seem to be a problem at all. The children call their father by the his first name and everything seems natural. This, then, begs the question why Atticus would want this. In my opinion, Atticus was trying to teach his children that he valued their opinion as if they were adults.