The name of the words

Which words? The ones following the verb on the right hand side of the equations? They're adverbs.

I'm not sure what the equal sign means. "Take" is not the same thing as "take away."

When we add up, on, down. up and the sense of a word changed.

Are you thinking of "modifiers"?

Exactly no. Now I believe, those words I showed in my first message are different. And we can't build new word with different sense by adding up, away and etc.

I'm sorry, but I don't understand. The words in your first message (away, up, down) all modify the verbs they follow, so they're all used as adverbs, and they all modify the sense of the verbs.

Perhaps if I knew what you mean by "build [a?] new word."

Ow. Modifiers, right, sorry. Misunderstood. So, what is about these ones?

"Ow" is a expression of pain. I hope you meant "Oh," an expression of recognition.

So, what is it that you want to know about "these ones," by which I assume you mean "away," "up," and "down"?

The main rules.

Do you want to know what position in a sentence modifiers may take with respect to the words they modify?
Do you want to know which modifiers are allowed to modify which words?

Yes I do.