Mar 9:40 For he that is not against us is on our part.
Alternative: For he that is not against us is for us.
The original Greek is much simply than the KJV translations, simply contrasting the two words "against" and "for."
The word translated as "on our part" is a simple preposition, huper that comes to English as hyper. Its basic meaning is to be "above" or "beyond" a thing, but a person who represents another was consider to be "above" the person or organization that they represented. In this sense, hyper means that the are acting "for" that person or "instead of" that person.
This meaning is a play on words, directly referring to the previous verse, because someone who represents another is said to act "in the name of" them.
So, in Greek, when someone uses power "in the name of Christ," we infer that they support, represent, and act in place of Christ.
"Against" is from kata (kata), which means "downwards," "down from," "down into," "against," "down toward," "opposite," "separately," "individually," "at a time," "towards," "in accordance with," "concerning," "corresponding with," "during the course of a period," and "severally."
"On our part" is from huper (hyper), which means "over" (of place), "above' (in a state of rest), "off' (ships at sea), "over" and "across (in a state of motion), "over," "beyond," "on behalf of one (metaphor), "for," "instead of," "in the name of," "as a representatitive of" (in an entreaty), "for" and "because of" (of the cause of motive), "concerning," "exceeding" "above" and "beyond" (of measure), "above" and "upwards" (of numbers), "before" and "earlier than" (of time), "over much" and "beyond measure" (as an adverb), "for" and "in deference of" (doing a thing), and "above measure."