Why did the children in to kill a mockingbird call their father by his first name?

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.