If they’re called kosher they legally have to be kosher.

That’s why Jewish-style delis are called “Jewish-style” and not “Kosher” if they’re not actually kosher. And spoiler alert, if a deli is called “Jewish-style”, it’s not actually kosher.

Kosher is a descriptor of the kind of food, like “halal” or “vegan” or “gluten-free”.

However, the reason Kosher Dills are called “Kosher Dills” is not because they’re kosher, nowadays most popular pickle brands of any kind are certified kosher, at least in the US. They’re called “Kosher Dills” because the specific type of dill pickle was introduced by Jewish immigrants and first sold by Jewish pickle-vendors.

It’s kind of like how Kosher Salt isn’t called “Kosher Salt” because it’s kosher. Halakhically, most salt is kosher and doesn’t even need a kosher certification if there’s no additives. Kosher Salt is called “Kosher Salt” because it’s the kind of coarse, large grained salt that is used by kosher slaughterhouses and butchers to salt and drain meat of blood. (Kosher meat must be drained of blood, using a process of salting and soaking, because consumption of blood is forbidden.)