The meanings of the names Vernon, Petunia, and Dudley were not chosen by J.K. Rowling for their meaning or significance.

The name Vernon is of English origin and means Alder Tree. Petunia is also of English origin, meaning "flower." Dudley also comes from old English and means "from Dudda's meadow." I believe the fact that all three of these names have botanical roots and reference to the outdoors is pure coincidence. It should be noted, however, that Petunia's mother clearly liked flower names because she named her other daughter Lily. It was Lily, of course, who grew up to marry James Potter and give birth to our protagonist, Harry.

In an article by J.K. Rowling published online, all is revealed regarding the significance of these names. She chose the name "Vernon" purely because it was a name she had always disliked. "Petunia" was the name always given to unlikable female characters in a game that Rowling and her sister used to play as children. While the article does not explain the reasoning behind the name Dudley, one cannot help but notice that the first half of this name is "dud;" a word which implies inferiority and a lack of wisdom.

The family surname, Dursley, was named after the market town by the same name in Gloucestershire, which is not far from where Rowling was born.