Greyhound Lane is in the centre of Wilton.
It’s probably named after the Greyhound pub which is close by, in the Market Place.
In times gone by, when many people couldn’t read, pubs were often named after things that could be visually depicted in a distinctive way – for example ‘Cross Keys’, ‘Red Lion’ or ‘The Dolphin’. I think ‘The Greyhound’ perhaps fits into this category – it’s one of the most easily recognizable of dogs.
Origin of the word ‘Greyhound’
The etymology of ‘greyhound’ doesn’t seem to be entirely certain – but there is a consensus that it has nothing to do with the colour ‘grey’. Wikipedia, for example.
Its origin does not appear to have any common root with the modern word “grey” for color, and indeed the Greyhound is seen with a wide variety of coat colors.
Wikipedia suggests that:
“Hund” is the antecedent of the modern “hound”, but the meaning of “grig” is undetermined, other than in reference to dogs in Old English and Old Norse. 
The Online Etymology Dictionary gives ‘grig‘ as meaning bitch, specifically
O.E. grighund, from grig- “bitch” + hund “dog” (see hound). 
I like one of the suggestions on the Greyhound Expressions website. The greyhound is a ‘sight hound’ – the dog has very well developed eyesight, and uses sight rather than smell for hunting. The suggestion is that:
Some believe it stems from the word “gazehound”, which is another word for sighthound.