‘For this reason the well was called Beer-lahai-roi (‘the well of the Living One Who sees me'). Consider, it is between Kadesh and Bered.'
We do not know whether this was a new name for the site or an old name applied to a new situation. It is possible that the name was originally given because it had been a lifesaver to someone who had arrived there in great need who gave credit to ‘the Living One' for deliverance. Alternately it could mean ‘the well of he who sees me and lives' referring to the well. It had no doubt been a lifesaver to many. But either way the name is given a significance, or a new significance, through Hagar's experience. If the name was old it was taken over and converted so that it represented Hagar's God.
“Between Kadesh and Bered” identifies its position to those unfamiliar with it, and shows the writer, or someone who added the description as a subsequent guide, knew it well.
The fact that this record is favourable to Hagar and yet retained in the covenant records of the tribe which became Israel, confirms its ancient origin. It was clearly recorded and kept in the tribe at a time when Hagar and Ishmael were an integral part of that tribe, and the probability must be that when Hagar returned to the tribe the covenant was immediately recorded as a part of God's covenant with Abram, by a sympathetic scribe selected by Abram.
God Expands His Covenant With Abram Under the Sign of Circumcision and Promises Prosperity to All his Descendants and a Son to Abram (Abraham) Born of Sarai (Sarah) (16:15-17:27).
Events have gone forward and with the birth of Ishmael things have become more complicated, so Yahweh now renews His covenant with Abram, bringing in Ishmael and promising the blessing of the birth of peoples and nations through him as well, while at the same time signifying that the promised line will be through a son of Sarai. This is thus an advancement on previous covenants. But at the same time the position of Ishmael within the covenant situation is made clear. He will enjoy the blessings of the wider covenant, but the original more direct and personal covenant is with Isaac (verse 21).
This change in emphasis is made clear in a number of ways. Both Abram and Sarai have their names changed, a sign of a new beginning, and Yahweh speaks as ‘El Shaddai' because He is speaking to a wider group than the original ‘chosen line', speaking to some for whom He will not be Yahweh, the personal covenant God.