The name Shaddai in the Bible
Shaddai is a divine name but not a creation name. It is first used in Genesis 17:1 where YHWH introduces Himself to Abram, saying "I am El Shaddai." God commands Abram to be blameless and promises him the covenant. Then He changes Abram's name to Abraham.
Etymology of the name Shaddai
The meaning of Shaddai is difficult to establish. The authors of the Septuagint and the Vulgate translated it with Almighty (pantokrator and omnipotens) but that's probably more out of enthusiasm than out of sound etymology (it really doesn't mean that).
It's possible that these authors deemed the name Shaddai so holy, that they circumvented it in a same way as the Masoretes would later do with the name YHWH (by pointing it as the word Adonai; hence giving rise to the pseudo-name Jehovah).
Some say that this name Shaddai (שׁדי) is derived from the verb שׁדד (shadad), meaning to destroy, hence: My Destroyer:
Others furiously refute this because this meaning would go against the nature of God. The prophet Isaiah, however, seems to be in the camp of the first when he writes, "Wail, for the day of YHWH is near. It will come as destruction (shad) from Shaddai" (Isaiah 13:6).
Those of the latter camp suggest that Shaddai comes from sadu, a word meaning mountain in the Babylonian (Akkadian) language that Abram spoke, and so El Shaddai would be El Of The Mountain, or El of the Gathering.
Yet another possibility is that Shaddai comes from שׁד (shed), the Babylonian version of the Roman genius; the house-spirit or one's personal protector spirit, the idea of which is not unbiblical at all, see Matthew 18:10 and Acts 12:15. The Babylonian depiction of the shedu, as they called it, had the familiar form of the winged bull. That would possibly relate our name Shaddai to the name Abir in essence, and would denote the "house-spirit" of Israel, which is also not unbiblical, see Exodus 23:23.
Some other ideas:
The rabbinic theory is that שדי may be formed by the particle ש, meaning who, which, or where, or that, plus the word די, meaning sufficient, enough:
Hence the name Shaddai also contains the meaning of Self-Sufficient. This is particularly interesting in light of Psalm 8:5.
שדי may even have to do with the verb שדה, meaning to moisten. God is after all the great Rain-maker (Genesis 2:6, Genesis 7:12, also see our article on the name Torah). It may even have to do with the derived noun שד, breast, bosom, used both in erotic scenes and the practical usage of feeding babies. A relation with the name Shaddai is not unthinkable, as this is the name by which God initiates the covenant of which Jesus is the final fulfillment. The apostle Paul compares introduction to the basics of the gospel with feeding milk to infants (1 Corinthians 3:1-2).
The name Shaddai may have originated in Akkadian, meaning Mountain, but to a Hebrew audience that hears God introduces Himself as El Shaddai, it must have meant My Destroyer, [Our] House Spirit, Self-Sufficient One, the Rain-Maker and Source Of Food For Babies, all at once.