A proper heir is the promise of both versions of the covenant, but the 1st version lists a slave, Eliezer of Damascus, as Abram's presumptive heir, without mentioning Sarai, Hagar or Ishmael. In the 2nd version, Abraham pleads for Ishmael to receive the covenant, but El Shaddai (an early name for God) specifies that Sarah (née Sarai) is to be the matriarch of the future multitudes, not Hagar.

Ishmael gets a consolation blessing, but no covenant.
#Bible

The renamings (Abram to Abraham, Sarai to Sarah) seems like an interpolation meant to harmonize related stories from two distinct oral traditions. Abram means something like "exalted ancestor", so the name itself may be figurative. The 2nd version is overtly interested in 1) justifying the monarchy, 2) isolating the Ishmaelites from the promise of an Israelite nation, and 3) making circumcision a prerequisite for inclusion in the nation.
#Bible

FWIW, there are lots of references to Abraham in Biblical books that scholars have dated as prior to the composition of Genesis, but according to Strong's Concordance, the name Abram only shows up in two Biblical verses outside of the Genesis narrative: one in 1 Chronicles and another in Nehemiah. Scholars date both of those books to after the composition of Genesis, and both verses identify Abram as Abraham. It looks like they're following the associated initiated by Genesis.
#Bible

I need to dig into the scholarship some more, but the explanation that makes the most sense to me is that there were two divergent traditions, one northern and another southern, about an "exalted ancestor" who makes a covenant with God, and that the composer of the Genesis narrative reconsolidated them by means of the Egypt detour and the conceit that Abram/Abraham and Sarah/Sarai were deliberate renamings rather than regional variants of the same words. That would serve the political imperative of culturally binding the northern and southern populations under the monarchy, and the success of that approach can be seen in the way subsequent authors affirmed that Abraham was originally named Abram.
#Bible

Sarai, btw, apparently meant "princess," which is suggestive in light of the pharaoh story. This is highly conjectural, but much as Abram is Abram because "exalted ancestor" is his role in the story, the name Sarai may point to an earlier version where her role is Egyptian princess who marries the exalted ancestor — a political arrangement that would bind the southern population to Egypt. An exclusivist Israelite monarchy would want to assert the priority of its claim over that of Egypt, so one function of the Egyptian detour in Genesis might be to refute that version of Sarai's story: to acknowledge the tradition that she left the Egyptian court with Abram, but not as a blood relative of the Egyptian monarchy.
#Bible

If you're curious, this is an interesting inquiry into the name El Shaddai, and how it compares to other names used for God in the #Bible: jstor.org/stable/1062160

Aside: I really wish it was standard for Biblical transliterate the different names for God, rather than translate them all into LORD or God. It's sometimes useful to know which name is being used.