Talking about the name of God is a sensitive issue because it is forbidden to use it in vain,and because people reject any interpretation different from the one they know, although that is more for the name YHVH than for ELOHA / ELOHIM, but I consider these as names of two different gods from different kingdoms, but that is another story and for the moment I will try to explain how of ILU AN, god of the sky in Sumerian (ELLU ANU in Akkadian) arises EL / ELOHA / ELOHIM god of Israel.
The origin of writing
Around 3500 BC the Sumerian proto script was pictographic and was written vertically from top to bottom starting from the right and then switching horizontally from right to left. The pictograms were written rotated 90 degrees to facilitate writing. As an example I can identify the symbol GUD = BULL that its pictogram is an ovoid figure with horns and turned with the horns to the left, from this the Phoenician alef arises and that the Greeks turned another 90 degrees forming the alpha letter A.
After changing the direction of writing from right-left to left-right, although the Hebrews and Arabs retain the sense of right-left.
But the cuneiform writing system was very complicated to write on papyrus, so other simpler systems such as the Ugaritic, Phoenician and many others were invented until reaching the alphabet I am using at the moment.
Deportation to NINIVE
During the Assyrian domination, King MENAJEM had a friendship policy with the Assyrians but not everyone agreed that they rebelled led by PEKAH son of ROMELIA and that led to the destruction of Israel and the deportation of its inhabitants.
During the deportation to NÍNIVE, those of Israel, THE INTELLECTUAL ELITE, learned from the Babylonian, Assyrian and Sumerian texts, coincidentally in NÍNIVE it was the library of ASURBANIPAL, and seeing how the god MARDUK son of ENKI, the powers of others Gods to defeat TIAMAT decided that their god should be superior to the other gods, so they removed his wife, children and lovers by gathering the qualities of those gods in ELOHA and in the place of their names the name ELOHIM was used.
Analyzing a little the creation poem we see that on day one where the messy and empty earth is mentioned subtly reference is made to TIAMAT the goddess of chaos, DARKNESS refers to APSU god of ABYSS and these two are gods of salt water (sea) and sweet, and continues to say that "the spirit of God moved over the waters (APSU AND TIAMAT)" giving a sense that ELOHIM is superior to these gods.
In another publication I will write a more complete analysis of "the creation's poem" and its comparison with scientific theories.
Building the name ELOHA
In the Akkadian and Sumerian texts it was customary to put the symbol DINGIR / AN (name in Akkadian and Sumerian respectively) before the names of the gods, this symbol has different phonetic values but in this case in Akkadian it is pronounced ELLU and it is translated as HOLY / HIGH / GOD and this symbol also represents ANU / AN god of heaven and by putting the symbol AN twice there is a REDUPLICATION that represents plurality, as in KUR-KUR which means MOUNTAINS, so AN-AN would mean GODS, That reminds me of ELOHIM in Hebrew which means GODS, but it could also be pronounced ILU AN in Sumerian (ELLU ANU in Akkadian) which translates as GOD AN or GOD OF HEAVEN more if I compare it with the Chinese in which the reduplication of the synogram ACTIVE It translates as VERY ACTIVE, so AN-AN would be GREAT GOD.
Now, if we take ELLU AN and write it in UGARÍTICO it would be something like ILUAN or ILWAN, my Ugaritic spelling is not very good but what matters is the idea, let's see that the N (NUN) in Ugaritic is similar to a type of H (KHA) but turning 90 degrees, look that in the Cyrillic alphabet, which is used for Russian and other languages, for N the H is used. Changing these letters results ILUHA or ILWHA.
But if we now invert the meaning of AH for HA, because of the change in the sense of writing from right-left to left-right, it gives ILUHA or ILWHA and if we finish it to Hebrew it was ELOHA, although ILUAH / ILWAH = ELOAH is also another of the names of the god of Israel, which has many names, also other gods like MARDUK or WOTAN TAUS (ODIN) have many names.