Firstly, YHVH is usually seen as the most divine, unpronounceable name of God, and it encompasses the elements (Yod = Fire, Heh = Water, Vav = Air, Heh sophith = Earth), and the Four Worlds, thus making it suitable for the elemental division applicable to the LBRP. But why is it in the East? Because the East is the traditional place of Light, of the Dawn, and of Divinity. The Adoration to the Lord of the Universe, for example, is done to the East, as are all other salutations in Golden Dawn work. The East is the station of the Heirophant, the initiator, who represents the greater initiator of God Himself.
Secondly, ADNI is employed in the South because it is, as Samuel Scarborough points out in his essay on the pentagram rituals in Issue 4 of Hermetic Virtues, "the place where the sun is at its utmost strength". The fiery nature of this quarter affirms God's aspect as Lord, a title perhaps fitting of the fiery Sephirah of Geburah (something we will explore in a moment).
Thirdly, AHYH is utilised in the West, the place of darkness (where the sun sets and diminishes), which, in terms of the four-fold division of Malkuth, borders on the realm of the Qlippoth, the "empty vessels" or "shells", demonic and destructive in nature. Given this, it is fitting to employ Ehyeh, the Divine Name of Kether, the highest Sephirah, to challenge and keep at bay the darkness that comes from the West. But this is but one aspect, for if we pay attention to the mystery of "Kether in Malkuth and Malkuth in Kether", realising that the Malkuth of Assiah could be seen as the Kether of a Qlippothic Tree, then this quarter is, effectively, the Kether of the Qlippoth, and thus it employs the Divine Name of Kether (Ehyeh).
This name is usually translated "I am", but perhaps more accurately as "I will be". This points to another hidden aspect of its attribution to the West, for, firstly, the Sun rises in the East and sets in the West. Thus, when it rises in the East (as YHVH), it instantly affirms its (and our) destination in the West by its Divine Name: "I will be". If that were not enough, however, let us remember the Lurianic teaching of the Shevirat ha-Kelim, the Breaking of the Vessels, which are the Qlippoth. These were the precursors of the Sephiroth, and thus this Divine Name again affirms, by this quarter's proximity to the Qlippothic realm, the future: the second attempt at Creation, resulting in the Sephiroth. The Light of God is not contained within the shattered vessels of the Qlippoth, but it "will be" contained in the future vessels of the Sephiroth.
Finally we have AGLA in the North, which is, akin to the above, the traditional place of "symbolic darkness" and evil. Thus, the force of Geburah is employed (via Gibor, which shares the same root), along with the title of Adonai, "Lord", which we saw in the South. Thus it can be seen that the potent fiery force of the South, where the Sun is at its zenith, is carried across to the North to face the darkness there. In this sense a line from South to North is drawn, just as one is drawn from East to West as mentioned given above. This creates an equilateral cross, symbolic of balance, but it is also a Solar Cross, for the circle is drawn around it by the magician. This is but one further reference to the hidden Tiphareth in this rite
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