Why is the use of the names Peter and Wendy for the two children in the story "The Veldt" significant?
I think Bradbury intends to contrast the cynicism and dark fantasy of Peter and Wendy from his story with the eternal innocence and positive fantasy of Peter and Wendy from Peter Pan. Instead of the children longing for a life of eternal childhood (as they do in Peter Pan), Bradbury's children scheme for ways to do away with their parents and are adultlike before their time. They have lost their innocence (because of an overuse of technology and psychological intervention) before they are out of childhood.
Bradbury seems to imply that if parents are willing to allow technology or "others" to raise their children, their children would be better off without parents (as in the "happy" world of Peter Pan).
I would say that the significance comes from the idea that both Peter and Wendy Hadley and Peter Pan do not (at least emotionally) have parents. While the Hadley children do have parents, their parents do not really care enough about them or pay enough attention to them and so they don't feel a strong attachment to their parents.
Because both the Hadleys and Peter Pan don't really know what love is (because of lack of parental love) they have become selfish. In Peter Pan, the selfishness is relatively harmless, but in The Veldt it certainly is not.
So the significance of the names is that it should point us towards these similiarities.