Why does it say "[Ki] No'atzu Lev Yachdav"?
Radak: These nations used to fight each other. Now they took counsel together against Yisrael. It says "Alecha", for they say that You cannot save us from their hand.
Malbim: This is the proof that they came primarily against Elokus. There were scattered nations - some were neighbors of Eretz Yisrael, and some were far away 1 . [Normally,] when neighbors take distant nations to help them, they have different purposes. The neighbors fight amidst fear, or in order to take their neighbor's land. The distant ones come for spoils. However, here their heart was unified - they had one purpose. Refer to 83:6:2:3.
Malbim (7-9): Edom, Mo'av, Geval, Amon, Amalek, Peleshes and Yoshvei Tzor were close; Yishmael, Hagrim and Ashur were distant.
What Bris do they make?
Rashi: It is to make Your name forgotten. You are not called Elokim to them, only to us - Elokei Yisrael.
Radak: It is to fight Yisrael.
Malbim: They are jealous of the publicity of Your Elokus in the world via Yisrael, and come against this.