The more precise term is soy milk skin. In consumer language, however, it is bean curd skin or tofu skin, and it is sold dried or fresh (frozen, in most cases).
In the photo above, the top two images show bean curd sheets in fresh and dried form. The lower left image is of dried bean curd noodles and the bottom right image shows dried bean curd sticks (yuba). The only other form of bean curd skin that I know of that’s not in the photo is bean curd pockets.
Dried tofu sheets
Bean curd sheets (sometimes labeled as tofu sheets) are used for wrapping meat or seafood. The stuffed tofu skin is either fried directly, steamed before frying, or fried before steaming, depending on the dish being cooked.
Dried tofu sticks (yuba)
Dried tofu skin in stick form, or yuba, is made by bunching the tofu skin. It is often cooked as a substitute for meat, especially chicken, which may explain why it is sometimes referred to as tofu chicken.
Like dried tofu skin sheets, tofu sticks must be rehydrated before cooking. Like real tofu which is flavorless but with the capacity to absorb flavors of ingredients it comes into contact with during cooking, one of the popular way of preparing tofu sticks is to cut them into bite-size pieces after rehydrating and braising in sauce to allow them to soak up the flavors of the spices and seasonings in the sauce.
Fresh tofu skin
Unless you live near a tofu manufacturer, chances are fresh tofu skin is available frozen. We used to buy it, four pieces per pack, from vegetarian food shops. That was when one of my daughters went vegetarian. Like dried tofu sheets, they can be used for wrapping food or cooked on its own.
Crispy tofu skin fingers with spicy honey lemon ginger sauce
Cakes of fresh tofu skin are cut into fingers and fried over low heat until golden and crisp. Make a no-cook sauce for dipping and you have a lovely snack or appetizer.
Dried tofu skin noodles
These can be served as a substitute for flour-based noodles. Just dump the dried tofu skin noodles in boiling water to soften and remove any funky smell, drain, refresh in cold water, drain and season.
Tofu skin noodle salad
Dried tofu skin shredded to look like noodles are soaked in soy-ginger-chili sauce then tossed with toasted sesame seeds and stir fried vegetables and Chinese sausages.