What is the exact technical word to describe the relationship between a verb and noun with the same root?

Solution 1:

Derivative:

(specialized language) a form of something, such as a word, made or developed from another form:

• "Detestable" is a derivative of "detest”.

(Cambridge Dictionary)

Solution 2:

A cognate accusative/object is a figure of speech in which the verb and object are etymologically related:

He slept a troubled sleep.
Dance a dance.
Die a peaceful death.

So there shouldn't be any problem writing:

verb x and its cognate noun

Since you're dealing with a language based on consonantal roots, “noun [derived] from the same root” would also work.

The problem with derivation alone is that it assumes that, say, the verb is historically prior to the noun, which may or may not have been the case.