El and Shaddai combined is not found many times in the bible - John Van Seters in The Pentateuch: A Social-Science Commentary, points out that each occurrence of El Shaddai in Genesis is within a doublet.
Then He said to him, "I am the LORD who brought you out from Ur of the Chaldeans to assign this land to you as a possession."
(Gen 15:7 TNK)
וַיֹּ֖אמֶר אֵלָ֑יו אֲנִ֣י יְהוָ֗ה
When Abram was ninety-nine years old, the LORD appeared to Abram and said to him, "I am El Shaddai. Walk in My ways and be blameless.
(Gen 17:1 TNK)
Another doublet, this with Jacob -
And the LORD was standing beside him and He said, "I am the LORD, the God of your father Abraham and the God of Isaac: the ground on which you are lying I will assign to you and to your offspring.
(Gen 28:13 TNK)
אֲנִ֣י יְהוָ֗ה
And God said to him, "I am El Shaddai. Be fertile and increase; A nation, yea an assembly of nations, Shall descend from you. Kings shall issue from your loins.
(Gen 35:11 TNK)
Then there are two versions of Isaac blessing Jacob -
And he went up and kissed him. And he smelled his clothes and he blessed him, saying, "Ah, the smell of my son is like the smell of the fields that the LORD has blessed.
(Gen 27:27 TNK)
בֵּרֲכ֖וֹ יְהוָֽה
May El Shaddai bless you, make you fertile and numerous, so that you become an assembly of peoples.
(Gen 28:3 TNK)
Personally, I thought this was cool -
God spoke to Moses and said to him, "I am the LORD.
(Exo 6:2 TNK)
וַיְדַבֵּ֥ר אֱלֹהִ֖ים
That only comes up two other times in the bible.
God spoke to Noah, saying,
(Gen 8:15 TNK)
וַיְדַבֵּ֥ר אֱלֹהִ֖ים אֶל־נֹ֥חַ לֵאמֹֽר׃
and before the Decalogue -
God spoke all these words, saying:
(Exo 20:1 TNK)
וַיְדַבֵּ֣ר אֱלֹהִ֔ים אֵ֛ת כָּל־הַדְּבָרִ֥ים הָאֵ֖לֶּה לֵאמֹֽר׃
Anyway, it's not clear what Shaddai means,
My beloved to me is a bag of myrrh Lodged between my breasts.
(Sol 1:13 TNK)
בֵּ֥ין שָׁדַ֖י
El Shaddai and Shaddai are not necessarily the exact same concept.
I saw an opinion that this is some real ancient shit but I'm not convinced. Exodus 6-3 is written when the three amigos were together, maybe it's from the Babylonian period. It is quite interesting to see those strands exposed.