What is a one-word sentence called?

An imperative sentence can be as short as one word, such as: "Go." Technically, a sentence must contain at least a subject and a verb, but in this case, the subject (you) is assumed and understood.

Just remember that not every one-word phrase is really a sentence. Let's look at an example: "She was unable to sleep. Again."

Here, "Again" is technically not a sentence since it's missing a subject (or a presumed subject like the imperative) and a verb. You can certainly write like this as you have the poetic and literary license, but the simple act of putting a period after a word does not a sentence make.