The area now known as “The Wish Tower Slopes” came about because a greensand outcrop formed a natural mound, surrounded by a lower-lying marshy area known as “The Wish” (sometimes spelt “The Whish”)
The name is thought to derive from the Saxon word for “marsh”, as is “The Wash” in Lincolnshire.
And so, when the Martello Tower was constructed, it took the name informally from the area it was built in, becoming “The Wish Tower”.
Officially, it is known as Martello Tower number 73 as each of the 74 towers in Kent and East Sussex were given numbers. The 24 towers built later along the east coast in Suffolk and Essex were assigned letters. You can find a complete list of the Martello Towers in the UK on the Geograph website.