All I can find on the book points to Elaine's mother being referred to by her last name only, Mrs. Risley. All of the parents are called Mr. or Mrs. in the book. I think it's because Elaine doesn't feel her parents helped her when she was being tormented by Cordelia and the other girls, and Mrs. Smeath is considered a mean, bad mother. Perhaps not giving them a first name shows how distant and lonely Elaine felt as a child and reflects how she felt about the adults in her life.
Go to the link below and you can read more details about the book.