JK Rowling is an author who seems to have taken pains to choose names for her characters carefully: wise Minerva McGonagall, severe Severus Snape, Sirius Black the black dog, Lupin the wolf, and so on. What about the names of her Muggle characters - in particular, those unpleasantest of Muggles of whom we see the most in the series, Vernon and Petunia Dursley and their son Dudley?
JK Rowling has answered this question herself in a Pottermore article on the Dursleys. The most interesting one is Petunia, whose name apparently comes from a half-remembered cartoon JKR saw as a child featuring an uncaring woman called Petunia. Quoting from the article itself (emphasis mine):
Vernon and Petunia were so-called from their creation, and never went through a number of trial names, as so many other characters did. ‘Vernon’ is simply a name I never much cared for. ‘Petunia’ is the name that I always gave unpleasant female characters in games of make believe I played with my sister, Di, when we were very young. Where I got it, I was never sure, until recently a friend of mine played me a series of public information films that were shown on television when we were young (he collects such things and puts them on his laptop to enjoy at leisure). One of them was an animation in which a married couple sat on a cliff enjoying a picnic and watching a man drowning in the sea below (the thrust of the film was, don’t wave back - call the lifeguard). The husband called his wife Petunia, and I suddenly wondered whether that wasn’t where I had got this most unlikely name, because I have never met anybody called Petunia, or, to my knowledge, read about them. The subconscious is a very odd thing. The cartoon Petunia was a fat, cheery character, so all I seem to have taken is her name.
The surname ‘Dursley’ was taken from the eponymous town in Gloucestershire, which is not very far from where I was born. I have never visited Dursley, and I expect that it is full of charming people. It was the sound of the word that appealed, rather than any association with the place.
While Rand al'Thor did a nice job catching his own softball, his answer makes no mention of Dudley Dursley's first name.
As revealed by Rowling in an early interview, the name Dudley comes from the name of a place she found on a map.
I kind of collect unusual names. You have to be very careful about telling me your name if you do have an unusual name because I'll probably put you in a book and I make a lot of the names up. But mostly maps. Maps are a great source for names. Dursley and Dudley and Snape are all, erm, places I can't visit anymore obviously.
Blue Peter (cBBC), 12 March, 2001
Rowling didn't specify which place, but a quick Google search for "Dudley UK" turns up this town, which is described as "a large town in the West Midlands of England, 6 miles (9.7 km) south-east of Wolverhampton and 10.5 miles (16.9 km) north-west of Birmingham."