As the tenacious eighty-year-old Granny Weatherall lies in her deathbed she experiences a stream of thoughts and memories, especially as she recalls her being jilted at the altar of her marriage. She has tried for sixty years to be rid of her memory of George, but she cannot dispel this "smoky cloud from hell that moved and crpt in her head...." When she tries to rise to pull down the shades, Granny hears someone say, "Mother, how do you feel now?" as someone places a cold cloth upon her face.
Hapsy? George? Lydia? Jimmy? No, Cornelia, and her features were swollen and full of litttle puddles.
It is probably this passage which mentions Granny's children that gives rise to the opinion that Granny has a son named George since she calls out in her mind the other children's names alongside this one. However, she does say the name of Hapsy, who has been dead right before saying "George." Perhaps, then, she merely calls to the dead before addressing the living, although she does not mention John.
When Cornelia tells her mother that the doctor is back, Granny's minds wanders back to Hapsy and she imagines that she speaks to her daughter. After Hapsy "melted from within," Cornelia asks her mother if there is anything she can do for her. Granny, in her mind, asks to see George. "I want to you to find George." This allusion to George, now, is clearly to the man to whom she was engaged. Thus, it seems that Granny's having called out the name George is simply a call for her former boyfriend.