Which fairy tale are the kids' names from?

Strictly speaking, the children's names don't come from any fairy tale.

They come from Peter Pan, which feels like a fairy tale because of how Barrie wrote it, but which is very much a modern story.

In Peter Pan, Peter is the boy who won't grow up. He is forever young and playful, almost a living archetype. This may be why he seems like something that might be found in a fairy tale. However, in Peter Pan, Wendy Darling is very different. She steps into the mother's place, being responsible for her brothers. Where Peter does not age, Wendy does. She matures, and leaves Peter further and further behind.

Bradbury's story reverses this. Peter and Wendy use the technology of the nursery to kill their parents, so that they can stay together forever, not having to listen to their parents. It is in many ways the ultimate rejection of parental authority, but also of maturation.