The LORD is a man of war: the LORD is his name. 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).