The Alter Rebbe explains the verse quoted at the beginning of the maamar: This is the meaning of what is written “On that very day (the 15th of Nisan) the entire ‘צִּבְּאוֹּת הוי '-Army of Hashem’ left the land of Egypt.” (Shemos 12:41) Meaning: Here the word “צִּבְּאוֹּת-Army/multitude of” is before the Name הֲוָּיָּ''ה, indicating that word “צִּבְּאוֹּת-Army” is secondary to the Name הֲוָּיָּ''ה, i.e., the Army of Hashem, the Jewish Army that belongs to Hashem, but it is not an expression of a descriptive title for Hashem as in the phrase “הֲוָּיָּ''ה צְּבָּאוֹּת-Hashem, who is the Master of the Armies.”
This is also a halachic distinction: in the phrase ‘צִּבְאוֹת הוי '-Army of Hashem,’ the word can (technically) be erased, since it is not considered a Name of Hashem. In contrast to “הֲוָּיָּ''ה צְבָאוֹת-Hashem, who is the Master of the Armies,” where the word צְבָאוֹת is holy as one of Hashem’s Names and may not be erased.
For, the phrase ‘צִּבְאוֹת הוי '-the multitudes belonging to Hashem’ mentioned in our verse refers to the ‘צִּבְּאוֹּת-multitudes’ of sparks of holiness that were sifted out from the exile of Egypt and were subsequently elevated to become included in Elokus as manifest in Atzilus, represented by the Name הֲוָּיָּ''ה, hence, the they are referred to as “צִּבְּאוֹּת הֲוָּיָּ''ה-the multitude of sparks that became included in Elokus of the Name Havaya.”
