A man of war - Compare Psalm 24:8. The name has on this occasion a special fitness: man had no part in the victory; the battle was the Lord's.
The Lord is his name - "Jah is His name." See Exodus 15:2.

The Lord is a man of war - Perhaps it would be better to translate the words, Jehovah is the man or hero of the battle. As we scarcely ever apply the term to any thing but first-rate armed vessels, the change of the translation seems indispensable, though the common rendering is literal enough. Besides, the object of Moses was to show that man had no part in this victory, but that the whole was wrought by the miraculous power of God, and that therefore he alone should have all the glory.
The Lord is his name - That is, Jehovah. He has now, as the name implies, given complete existence to all his promises. See Clarke on Genesis 2:4 (note), and Exodus 6:3 (note).

The LORD [is] a (c) man of war: the LORD [is] his (d) name.
(c) In battle he always overcomes.
(d) Always constant in his promises.

The Lord is a man of war,.... A "man", which has respect to the future incarnation of Christ, for as yet he was not really man; though it was purposed, covenanted, agreed to, and prophesied of, that he should, as he after was; not a mere man, as appears by the following clause: "a man of war"; or a warrior; being engaged in war, and inured to it; having to do with very powerful enemies, Satan and his principalities and powers, the world, and the great men of it, antichrist, and all the antichristian states. A warrior well versed in all the arts of war, and abundantly qualified for it, having consummate wisdom, strength, and courage, and thoroughly furnished and accoutred for it; having on the breastplate of righteousness, the helmet of salvation, the garment of vengeance, and cloak of zeal, and a vesture dipped in blood; and with a sword girt on his thigh, or drawn, or coming out of his mouth; and with a bow and arrows, going forth conquering, and to conquer; for he is a victorious one, who has conquered sin, Satan, and the world, and will subdue all others, and make his people more than conquerors, through him. He is not a common man of war or warrior; he is the Captain of the Lord's host, the Leader and Commander of the people, the Generalissimo of the armies in heaven and earth, and is a Prince and King at the head of them:
the Lord is his name; or Jehovah, which proves him to be more than a man; and being so, it is no wonder that he is so mighty, powerful, and victorious.

The Lord is a man of war - Able to deal with all those that strive with their maker.