What is the name for the grammatical device of putting "not" after a verb to negate it?

The syntax of "N V not" ("I know not") in English is called simple negation. It was much more common in Early Modern English.

The negation pattern that is more commonly used now, "N do not V" ("I don't know") is called just plain negation (it is the unmarked (expected) form).

The mechanical change from the verb+not form to do not+verb form that you ask about works ok for the vast majority of verb+not cases I've encountered. But some instances break. For example, "Imagine not being at home" typically is a suggestion or command meaning "Imagine what it would be like if you were not at home." That is somewhat different than the command "Do not imagine being at home."

This instance illustrates that slightly more context or information than verb+not is required; the example's form actually is verb+not+gerund and not modifies the gerund rather than the verb.

Note, although the mechanical change fails for many verb+not+gerund cases, it works ok for some. Example: "Fear not being sad" has exactly the same meaning as "Do not fear being sad", except on those occasions when it has the meaning "Be afraid of not being sad".