Why doesn't Daisy refer to her child by name or heed her child's 'reluctant glance'?

Daisy Buchanan is shallow and self-centered. Things and people are really only important in her world if they can make her feel good about herself. She is not a good mother, ignoring her daughter Pammy repeatedly throughout the book. The girl is essentially being raised by a nanny. She is paraded in front of guests when there is some reason for a display of how wonderful everything is in Daisy's world. Daisy hopes Pammy will become "the best thing a girl can be in this world, a beautiful little fool".

This is one of the ironies in The Great Gatsby. Jay Gatsby has spent his entire life becoming the person he thinks Daisy would want. He even takes the blame for the hit-and-run death of Myrtle when it was really Daisy driving. He pays for this with his life. This is his ultimate gift to Daisy, a woman who was really not worth his devotion.