Therefore, the Divine Name הוי' can be found joined with all other Divine Names, as it is written (Bereishis 2:4) “[and it was] on the day that הוי' אלקים made the earth and heavens etc.” and it is written (in many verses) “הוי' צבאות,” (showing how the Name הוי' becomes invested in the Name אלקים and in the Name צבאות).
Because it is the Name הוי' that draws down from the Infinite Light of Hashem to become invested into the Names of אלקים and צבאות, which refer to (the outer aspects of) the Keilim of the Sefiros of Gevura and Malchus, as well as into the Keilim of the other Sefiros.
And so, the Name הוי' is the intermediate level between His Infinite Light (that completely transcends the Sefiros) and the actual “limitation,” as it were, of (the outer aspect of the) Keilim. Therefore, it can bind together the Infinite Light with (the outer aspect of) the Keilim.
Now, it is written (Shemos 3:15): “This (Name הוי') is ‘שמי-My Name’ forever, and this is ‘זכרי-how I am to be called’ [throughout all generations].”
It is explained in the Tikunei Zohar (4b): The numerical value of the word ‘שמי-My Name’ combined with the Name י'ה (which are also the first two letters of the Name הוי') equals 365, corresponding to the number of the prohibitive mitzvos in the Torah; and the numerical value of the word ‘זכרי-how I am to be called’ combined with the last two letters of the Name הוי', which are ו'ה, equals to 248, referring to the number of action-based mitzvos of the Torah.
Thus, the Torah as a whole, the 248 action-based mitzvos and the 365 prohibitive mitzvos are rooted in the letters of the Name הוי', as they are manifest in Ze’eir Anpin (the emotional attributes of Hashem as expressed) in Atzilus:
Specifically, the 248 action-based mitzvos are connected to the attributes of Chesed-Kindness of Ze’eir Anpin of Atzilus; and the 365 prohibitive mitzvos are connected to the attributes of Gevura-Severity of Ze’eir Anpin of Atzilus.
In this totality is included the particulars of the laws of the Torah, that which is prohibited and that which is permitted, fit for use or unfit, guilty, or meritorious, and so forth.
That which is permitted and fit for use stems from the attributes of Kindness of Ze’eir Anpin (of Atzilus), and one who transgresses a prohibitive mitzvah, brings upon himself severity from the attributes of severity of Ze’eir Anpin thereby deserving punishment etc.
And it is (through the Name הוי') that the Infinite Light of Hashem becomes invested in (the outer aspect of) the Keilim of Ze’eir Anpin, until “Hashem’s Infinite Light unifies with the Keilim of Atzilus,” as mentioned before. This is the “function,” as it were, of the Name הוי' in the context of uniting the Infinite Light with the Sefiros.
With this we can understand why the Name הוי' צבאות is not mentioned anywhere in the Chumash, only the Name הוי' by itself (or combined with other Names, but not with צבאות), and only Chana was the first one to have called Hashem by the Name “הוי' צבאות.”
