While I haven't found the reason for the name (they don't taste like fried chicken or have much flavor) I am guessing it is the texture which is crunchy.
This site writes
"Fried chicken mushroom is considered second-rate, and it is when you sauté it with onions and garlic. But Asian cooks consider it first-rate because that's how it tastes when they use it correctly—in soups, stew, and sauces. Its sweet flavor, chewy texture, and slight okra-like thickening effect make it perfect for such dishes. "
Well, I fried it so I might buy it again and try it in a soup.
It also seems to be used in Eastern European recipes
Polish Marinated Fried Chicken Mushrooms
Slovenian "Chicken" Goulash
Scientific name: Lyophyllum decastes