chapotraphouse

Apparently it's because it has higher milk content than their previous failed milk chocolate bar, but also they tried a bunch of names with it:

Through its development, the bar was variously called 'Highland Milk', 'Jersey' and 'Dairy Maid'.[2][5] Accounts on the origin of the Dairy Milk name differ; it has been suggested that the name change came about on the advice of a shopkeeper in Plymouth, but Cadbury maintains that a customer's daughter came up with the name.[2][5]

Also in 2010 they changed the shape to reduce the weight without reducing the price (capitalism efficiently reducing the treats) and everyone complained the new shape tastes sweeter.