In Korean, the story is called 호랑이와 곶감. I would personally go with the translation: “The Tiger and the Dried Persimmons", but this isn't the exact translation.
First, I’ll address the food, because it’s simpler. In Korean, it's called 곶감.
There are actually four types of persimmons enjoyed in Korea, but I'll just explain the two types.
Regular persimmon is called "단감" (fuyu persimmon): 
As a fun fact, at least back when I was a kid, the color orange is more commonly associated with this fruit than the orange fruit itself!
When you leave this specific variety of persimmon outside to dry for weeks during the end of fall/beginning of winter (around the first or second week of November, it's considered winter there), the water basically evaporates and sugar builds until it literally becomes like a raisin. Except it's WAY better than raisins. You can look up pictures online. The white stuff you see on the surface is actually sugar from the persimmon! This variety is called 곶감 in Korea, like in the title of the story. (As a quick aside, I have no clue why it's called the way it is. I always just assumed it's because it kind of looks like the word 곶?)
Regarding the actual language:
The most literal translation of this title would actually be “Tiger and Dried Persimmon” or “Tiger and Dried Persimmons” (though 와 by itself can also mean "with"). You see, Korean doesn’t have articles such as “a”, “an”, and “the”, and they also don’t really have plural forms. The importance of how one knows something is plural is MOST dependent on the context that is given. Take this question for example:
Do you have a child?
Do you have children?
In Korean, this is just,
자녀 있어요?
It's translated as "children" but it can also just be "child". That's why I say it's either "persimmon" or "persimmons".
What about the tiger though?
You can assume that there is just one tiger in this story. It's due to the first part "호랑이와". If there were more than one, normally it would specify (다섯 호랑이와; "Five Tigers and....") or a more general plural (호랑이들와). But adding "들" is normally only for talking about a general plural number of tigers, not as a result of an inflection. The usage of "들" is kind of situational and also doesn't apply to every noun (I can't think off the top of my head the ones that work) and it's only to make sure that people know there are more than one of the subject discussed.
The reason why the plurality doesn’t really matter with the persimmon is that the story doesn’t really change whether there was just one persimmon or ten. The idea is that the Tiger was scared away by something as trivial as a persimmon out of ignorance.
So why would I go with the plural form of persimmon? Because typically in English (from my knowledge) you use plural form when there is an unspecified or unknown amount of something (whether there is just one or not). It’s like how you ask “Do you have children” as opposed to “Do you have a child”. Since Korean doesn’t differentiate between most plural forms, I’d just go with the plural. Add the articles for the sake of grammar.
