Whitener is known as nai3-jing1
"essence of milk" in Chinese
. I have seen it under the brand name "Coffee White", though there are many other varieties. It is also widespread in Japan
It is a much brighter white than any form of real milk or cream that I have seen in the U.S. When you first pour it into coffee it behaves a bit like half-and-half in that a little of it floats on the surface of the coffee while the rest disappears into the black. I don't notice any particular effect on the flavor of the stirred coffee, although by itself coffee whitener is vaguely sweet.
Asking for milk with your coffee in Taiwan almost always gets you whitener. If you ask expressly for fresh milk you will get a little glass of it along with a surprised expression. Although coffee has grown greatly in importance in Taiwan since I first started visiting in 1984, and although Starbucks-style coffee drinks made with foamed milk, such as cappuccino (ka3-bu4-qi2-nuo4 and other names) and latte (na2-tie3 "get some iron"), have invaded even the smaller Taiwanese cities since the mid-'90's, I don't think the sovereign position of whitener as the sole consort of black coffee has been much threatened by fresh milk.