The marketing must be working, because I've seen at least one Brit use "Dairy Milk" as a synonym for milk chocolate. This was on some forum years ago, they were complaining that when they visited the USA they weren't able to find dairy milk at the grocery store. All the Americans in the thread were like "wtf are you talking about, every grocery store sells milk," and it took some back and forth for everyone to understand each other.

It also seems a bit redundant, like saying "vegetable broccoli" or "pasta spaghetti."

[–] Awoo@hexbear.net 3 points 3 weeks ago

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.