* In Japanese folklore, the nine-tailed fox is often referred to as a kitsune**, which is the general term for fox in Japanese. They don't always have names, and can even change their names at will.
* In the Pokémon franchise, the nine-tailed fox is called a Ninetales**. This is its official name, but it may have other nicknames depending on the specific Ninetales.
* In other cultures, the nine-tailed fox is sometimes called a huli jing (Chinese), kumiho (Korean), or gumiho** (Korean). These are general terms for the creature, and specific individuals may have unique names within their respective stories.
So, to answer your question more definitively, a nine-tailed fox does not have a universal name. It can have a name in specific stories, but the name will vary depending on the context.