My question is not why they call their father Atticus as much as why he lets them do this, and what this says about their characters.
Where I come from--and, I think, in 1930s Alabama--it is not common to let kids call their parents by their first names. Usually the parents stop this from happening, and Atticus presumably made a decision not to stop them. Why did he make this decision, and what does this say about his character?
Lee does this to paint the whole Finch family as unconventional, reflecting upon the abnormal characters of Atticus, Jem, and Scout. In southern Alabama during the 1930's, society isn't very progressive, shown by the townspeople's negative attitudes towards African Americans. Similarly, in this setting, society expects children to address their parents with respect.
It is within this society that the dynamic character of Atticus Finch is developed. In contrast to the other townspeople, Atticus is highly educated and progressive, defending the rights of the unrepresented. He wants his children to grow up with a forward-thinking mindset, just like him, questioning the world's opinions through rational thought and reason. Thus, one step towards doing this is to address their father as equal, showcasing Atticus's belief that all men are equal, regardless of age, gender, or race. For the exact reason of highlighting the unorthodoxy of the family, Jem and Scout call their father Atticus.
