Why is the use of these names for the two children in "The Veldt" significant?
The use of the names of Wendy and Peter in the story The Veldt,by Ray Bradbury, is significant and indeed somewhat connected to the use of the same names in the characters of the novel by J.M. Barrie, Peter Pan.
However, the connection between the names is less literary and more psychological. In the story The Veldt Peter is a little spoiled brat. He is intelligent but extremely immature. He does not have any regard for his family, and he controls his everybody with both his wits, and his willfulness. Nowhere in the story do we see a chance for Peter to act any better. He is completely flat in that there is no growth inside him, and therefore, no change in his character.
Similarly to the so-called "Peter Pan syndrome", the character of Peter is the typical male that refuses to take responsibility for his actions, who acts like a spoiled child, and who can never change his ways.
Similarly, the name of Wendy comes from yet another complex in women called the "Wendy Complex". The name comes from the story Peter Pan, since Wendy represents the motherly figure that the children in Peter Pan needed so much, and which Wendy somewhat fulfilled. In the case of The Veldt Wendy similarly adopts a protective role towards her brother, but she enables and spoils him by doing whatever he asks her to do. She has a terribly misguided idea of what her role is within her family, and towards her brother. Therefore, she is actually sort of his psychological slave even allowing him to dominate her to the point of setting up her parents to their deaths.