We never learn the first name of Atticus' wife, Scout's mother. What Scout does reveal is this in the firs chapter after she tells us all about Calpurnia's presence in their home:
Our mother died when I was two, so I never felt her absence. She was a Graham from Montgomery; Atticus met her when he was first elected to the state legislature.
Heritage was very important in Maycomb County. You will find as the book continues that Aunt Alexandra feels that Jem and Scout were carefully bred by a process called gentle breeding. This means since Atticus was a well-to-do man, his wife was from a high class family too, they were from Montgomery and her last name was Graham.
I think Lee never reveals a first name for a couple of reasons. First, the death of the mother is a fact, a detail and a circumstance of life. I don't think Lee wanted another persona hanging around the storyline. Jem thinks of her enough. Also, having a greater identity of this dead woman would certainly bring her into the story among the women of the town and certainly Scout. To have explained her anymore would be more detail than this already jam-packed novel could handle.
The first name of Scout's mother is not revealed in To Kill a Mockingbird. Her maiden name was Graham before she married Atticus and became a Finch. Very little information is given about her in the story. The primary reason for this is because the narrator, Scout, has no memories of her mother. Scout had been only two when her mother passed away from a heart attack. Her heart condition was hereditary. Her young age caused Scout to later say that she "never felt her absence" (Chapter 1).
When Scout's mother and Atticus got married, he was a middle-aged man. She was fifteen years younger than him. She was from Montgomery, Alabama, the state capital. Scout does not miss her mother like Jem does. Sometimes he remembers her and wants to spend some time alone. Uncle Jack once tells Scout that she resembles her father more than she does her mother. Mrs. Dubose recalls Scout's mother as being a lovely person. Scout also hints at what her mother had looked like:
Jem's soft brown hair and eyes, his oval face and snug-fitting ears were our mother's... (Chapter 15).
In Go Set a Watchman it is revealed that Atticus Finch's late wife was called Jean, not Louise as many had previously thought due to Scout's middle name.