I know however that the four names for God oftentimes are used in traditional protective circles in medieval grimoires, i.e. they have a traditional protective value in the minds of the magicians.
Personally I believe that the Lesser Ritual of the Pentagram should be regarded as a general ritual of banishing and invocation (especially of the former). The four traditional Qabalistic divine names in the ritual doesn't necessarily pertain to the four Elements themselves, but instead they may be used to invoke divine power or current of a more neutral (i.e. general) nature, not Elemental per se.
IHVH (Tetragrammaton) is one of the most recurrent and important names for God in the Old Testament. Adonai is used as a substitute for it - remember Jews were forbidden to pronounce the name Tetragrammaton - designating him (i.e. IHVH) as "Lord". Even the dagesh points (i.e. vocal punctuations) were taken from the name Adonai and applied to IHVH, resulting in the vulgar pronunciation of "Yehowah" or "Yahweh". Eheieh is God as the burning bush - "I am who I am" - as He appeared for Moses. AGLA is once again a reference to Adonai - "Lord" - as it is a acronym for "Atah Gibor LeOlam, Adonai" which can be translated as "Thou art powerful for ever, Oh Lord". So all this points to the One God, not the many; i.e. unity.
Thus, read as one sentence one gets "IHVH, Adonai, Eheieh, Atah Gibor LeOlam, Adonai" which may be translated as "Yehovah, my Lord, who are who You are, Thou art powerful, Oh Lord, through the ages". So what we basically have here is a prayer that invokes the power and grace of God Almighty.
Another analysis of the names is that the Lesser Pentagram Ritual uses one active (IHVH) and passive (Adonai) name of the Elemental Pentagrams, i.e. from Air and Earth respectively, and also the active (Eheieh) and passive (AGLA) spirit pentagram names, in succession. Active - Passive - Active - Passive. Maybe something can be construed from this?
Be there as it may, but I get a sense of a general feeling with these names, as opposed to the specially allotted Elemental divine names as they appear in the Greater and Supreme Pentagram Rituals.
But all this is my personal speculation, and as I am not sure of what the original intention was in alloting these names to the Quarters I wouldn't tamper with it. Something we don't know anything about may be lost, and the new insertions could create something that was not originally intended.
The particular names for God in the ritual also alludes to the four Elements - the elemental world of matter - as the Tetragrammaton (IHVH) works as the primary name, being spelled first, and the general use of Adonai as a substitute for IHVH. But curiosly enough, all the names used in the Ritual are Tetragrammata, i.e. they each consists of four letters; IHVH (Jehovah), ADNI (Adonai), AHIH (Eheieh) and AGLA (Agela). All this points towards the overall and general Elemental (material) attribution of the ritual.
In the same manner, the Lesser Hexagram Ritual also works as a general banishing ritual for more exalted forces, i.e. beyond the sublunary world, attributed as it is to a overall and general Planetary (astral) nature; it uses the sevenfold lettered name of ARARITA. In the same manner Saturn is here used as a general representation for the astrological forces (as opposed to the terrestrial) as it corresponds to Earth; the 32nd Path of Tau - Earth and Saturn.