As others have noted, the names Peter and Wendy Hadley in Bradbury's 1950 story are inspired by J.M. Barrie's 1904 Peter Pan. Barrie's Peter Pan and Wendy Darling are a bit different than Bradbury's, however, given that Peter Pan does not wish to grow up and never does, while Wendy Darling leaves him after a time to return to her family.

In Bradbury's story, Peter and Wendy remain in the state of egocentrism that psychologists observe that most well-adjusted adults outgrow. Egocentism that persists in children into their adolescence can, many psychologists observe, be caused by perceived parental rejection.

As created by Bradbury, Peter and Wendy Hadley might well believe on some level that their parents have abandoned them to the machines that see to their daily needs. When their father begins to set limits for them, the children have become so entrenched in their egocentric existence that their parents become a threat to their autonomy. In Bradbury's dark tale, the parents are therefore permanently removed by Peter and Wendy.

On a psychological level, Barrie's Peter is not all that different than Bradbury's, in that he is self-absorbed and lacking in empathy, perpetually living in the moment rather than contemplating the past or the future.

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.

Why are the children's names significant in "The Veldt"?

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.