Evidently the parents named the children Wendy and Peter Pan because they wanted them to be free and happy and to indulge their fantasies like their fictional prototypes. The girl named Wendy and the boy named Peter Pan in J. M. Barrie's play live in a fantasy world in which they are able to fly and to become involved in all sorts of exciting adventures. The Wendy and Peter in Ray Bradbury's story "The Veldt" are doing pretty much the same thing in a high-tech, futuristic home where everything is done for them by machines. Ray Bradbury was an American writer, but he intentionally makes the Hadley family, and especially the two children, sound British in order to suggest the parallel of his story with the English story of Peter Pan. For instance, the children call George "Father" rather than "Dad"; Peter says, "I thought we were free to play as we wished"; "That sounds dreadful!"; and "I'm sure you're mistaken, Father." Throughout the story Bradbury's Peter and Wendy sound like upper-class English children of J. M. Barrie's Edwardian play. At the very end Wendy politely offers David McClean the psychologist a cup of tea.
Wendy and Peter in "The Veldt" are modernized versions of Wendy and Peter Pan in J. M. Barrie's stage play Peter Pan, or The Boy Who Wouldn't Grow Up (1902). The big difference is that Bradbury's Wendy and Peter are real children, not fantasy children. They have been so badly spoiled that their parents, George and Lydia Hadley, have completely lost control of them. The children are controlled by machines, and the machines are controlled by the children's fantasies.
Ray Bradbury (1920-2012), who had a fear and loathing for machinery, may be exaggerating--but, on the other hand, he may be predicting the future with uncanny accuracy. The danger to the children, and to society, may be greater than the danger to the parents. If children grow up having everything done for them, then when they become adults they may not be able to do anything for themselves.