Sorry if this is a little disjointed - I'm picking a few short sections from my paper on this.
Actually
Israel is related to Sarah/Sarai. I -Sra - el. These go back to a Sun Goddess.
ORAH: Variant spelling of Hebrew Ora, meaning "light."
The name Sarah is identical to the Hebrew noun שׂרה (sara), ... a similar root-verb in Assyrian, sararu means to rise in splendor (of the sun.)
www.abarim-publications.com/Meaning/Sarah.html
“The two forms of the name, "Sarah" and "Sarai," are identical in meaning; it is difficult to understand the reason for the change.
"Sarai" is probably the more archaic form of "Sarah," though the termination "ai" is unusual in the feminine. The writer of Gen. xvii. 15 must have considered the "ah" of "Sarah" as implying in some way "yahu" or "yah" (the "Yhwh" element). Accordingly, the change would be similar to that of "Joshua" to "Jehoshua." Perhaps it was the intention to read the name
"Sarayahu," the "hu" being added to "Sarai." In that case
the meaning "princess" now given to "Sarah" must be abandoned. The element
"sarah" is identical with a part of the name "Israel," and "Sarah" and "Sarai" are appropriate names for Israel's mother (Isa. li. 2; comp. Robertson Smith, "Kinship and Marriage," p. 30; for the forms see Olshausen, "Lehrbuch der Hebräischen Sprache," § 110; Nöldeke, in "Z. D M. G." 1886, p. 183; 1888, p. 484; König, "Historisch-Kritisches Lehrgebäude," II. i. 427). The name "Sa-ra-a" is reported to occur in Babylonian tablets (Cheyne and Black, "Encyc. Bibl." iv. 4285, note 3).”
Even Rabbinical material associates her with great bright light.
In Pharaoh's Harem.
On the journey to Egypt, Abraham hid his wife in a chest in order that no one might see her. At the frontier the chest had to pass through the hands of certain officials, who insisted on examining its contents in order to determine the amount of duty payable. When it was opened
a bright light proceeded from Sarah's beauty
Some think Abraham and Sarah represent two tribes coming together with Sarah's, being matrilineal, and linking to a Sun Goddess. And they birth Israel.
(2) …Tribal antipathies and sympathies, and political and racial interdependence and kinship, are expressed by them; but frequently, in order to complete a system, an individual ancestor or eponym is invented. While some of the names that occur are clearly those of clans, or of localities, Abraham = Abiram is not. It seems to be an appellative; but it is connected with Hebron, an old center.
Sarai = Sarah, on the other hand, is the name of a clan—Israel. As Jacob became Israel in another cycle (with Beth-el), so here Abraham (Hebron) is connected with Israel. This is the meaning of the marriage of Abraham with Sarah, as similar ethnic or historical data underlie the story of his dealings with Hagar and Keturah.
“(4) Originally,
Canaanite local eponyms connected with Israel; the Patriarchs were later ranged and ranked systematically, so as to establish an exclusive descent for Israel and disclose its distinction as the people of Yhwh. In this scheme Abraham becomes the "great ancestor" (Abram), or "the ancestor of many nations."
Through his wife Sarah he begets the Isaac-Jacob tribes, or Israel (= Sarah); and through his concubine Hagar he begets Ishmael, who therefore is marked as lesser in her degree of purity.
SARAH (SARAI) - JewishEncyclopedia.com
Variations of Both names, Abraham and Sarah, are found on Babylonian tablets.
Encyclopædia biblica: a critical dictionary of the literary, political and ... - Google Books
Again - sorry it is so jumbled. LOL!
I tried to include some of the Jewish sources.
In other words, basically, Sarah/Sarai means Bright Sun - and is imbedded in Israel- whom she gave birth to.
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