It is notable that the majority of the characters in Flannery O'Connor's short story that do not have names are women. The grandmother is sometimes called the old lady, but she has no first name or surname. The same is true of her son Bailey's wife, who is sometimes called "the children's mother." Red Sammy's wife is identified in no other way than as the marital appendage of the proprietor of The Tower. The baby that belongs to Bailey and his wife also has no name.
Taken together, this could suggest that women of any age and babies are so inconsequential in Southern society that their individual identities are of no importance. They are instead identified by their roles: grandmother, mother, wife, and child. The fact that June Star, a young girl, has a name could indicate that until she is of marriageable age, she has some value, perhaps as a familial bargaining chip for something like a dowry. Likely, then, her name would fade when she married, unless Southern society had changed by then.
The only other character without a name is the murderer, the Misfit. Unlike the other men in the story, he has no name. This could be because he does not fit the role of conventional Southern men. As an outlier and a criminal, he has sacrificed his reputation, thus his name, and is therefore diminished to a derogatory term. His outsider status is only deepened by the unthinkable horrors he enacts upon Bailey's family.