What is the name of this Chinese Fish Soup where guests cook their own fish in broth? One of my friends tells about some kind of a delicious fish soup that he ate in china. But he doesn't know the name of the dish.

It was served in a big bowl in the center of the table (in a restaurant). The bowl is heating, and it's a soup that does not contain any fish. Some pieces of fresh cleaned fish are in front of each person, so he can put it in the soup, and after a minute, the fish is ready to be eaten.

Do you know the name of this food?
Sounds like hot pot.

There are a zillion variations, with different kinds of broths and different things to cook in it, so I don't think there's any one recipe name you could search for to duplicate exactly what your friend had. It's possible that knowing the region he was in would allow some informed guesses from folks with some local knowledge (not me). Note that it's common to cook a lot of different things in the broth all at the same time, not just one thing per meal.

So if you want to try to make something similar without a lot of work, I suspect you'd just want to a broth you like (or a soup base from a Chinese grocery store - hot pot is popular!) and whatever simple fish sounds good to you. If you want more elaborate things, try Google; there's too much variety for us to try to cover it here.