In short, when Nora references her old friend from school, now Mrs. Christine Linde, her own husband, Torvald, does not recognize the name while a mere family friend, Dr. Rank, does. This shows just how little Torvald cares about or attends to the things that his wife tells him. Dr. Rank, who we find out much later has long been in love with Nora, does seem to remember even the least significant things that Nora has said to him, showing how much more he does listen to her than her own husband does. It is ironic that Torvald, her husband, would listen less to her than one of his friends does, as we would perhaps think that Torvald married her because he loved her, and if he loves her then he would surely be interested in the things that she says, in her life, and so on.
This small episode would seem to indicate that Torvald really does not love Nora for herself—a suspicion for which greater proof will come in later scenes—but rather for her looks and her apparent obedience to him. When he learns that she was disobedient and took out a loan against his wishes years ago, he speaks cruelly to her and tells her that she will no longer be able to see their children. This is not really very loving. His failure to recognize Mrs. Linde's name is an early sign of this.