I am hesitant in using an article after the sentence which we call.
We discovered a new attack model which we call "man-in-the-middle" attack
We discovered a new attack model which we call a "man-in-the-middle" attack
For your particular example I think the sentence should have a definite article. The name of the model is being given, so it uniquely identifies the model and so should have a definite article. Extending this for your situation you might have:
We discoved a new attack model which we call the "man-in-the-middle" attack. A man-in-the-middle attack is characterized by ...
So the model has a definite article, but the actual attack (of which there may be many different instances) has an indefinite article.
In the examples you give, all three options are possible and idiomatic. Which one you prefer comes down to a matter of choice, context and emphasis.
If you change the sentences while keeping the phrase, the three constructions might be:
The soldiers favoured the model known as man-in-the-middle attack.
The man-in-the-middle-attack proved the most successful model throughout the war.
The high command favoured a man-in-the-middle attack to surprise the enemy.
In most examples, it is possible to either change the article, to omit or to insert it. It's whatever comes as most natural to the speaker or writer in context. There is no rule governing the use of the article.