Was Beersheba named by Abraham or by Isaac?

Both did, and chapter 26 shows why. Abraham gave the name first, after he and Abimelech swore a covenant over a disputed well, sealed with seven ewe lambs (21:25–31). Beer-sheba means ‘well of the oath’ or ‘well of seven’; the Hebrew verb for swearing (shava) is related to the word for seven (sheva). Genesis goes on using the name from then on: Abraham “dwelt at Beer–sheba” (22:19), and Isaac “went up from thence to Beer–sheba” (26:23) before anything happened there in his own day.

In the meantime the Philistines had stopped up Abraham’s wells. Isaac dug them again, “and he called their names after the names by which his father had called them” (26:18). At Beersheba history then repeated itself. Abimelech came to Isaac, an oath was sworn, and on the same day Isaac’s servants found water in a well they had dug (26:26–32). Isaac called the well Shibah, ‘oath’, and the writer adds that this is why the city is called Beersheba to this day. Keil reads this as confirming the old name, not replacing it: Isaac’s treaty renewed Abraham’s, and so the name was renewed too. Haley notes that in the East an old name was often renewed with fresh meaning by a new event.

Which well?

Adam Clarke thought Isaac’s well was probably Abraham’s own, stopped up by the Philistines and opened again, with the old name restored to it. Keil thought it was a second well, noting that two ancient wells were still to be seen at the site. Either way the name was renewed, not invented.

Two sources

Many critical scholars see the two chapters as two versions of one tradition about the naming of Beersheba. Keil replied that the circumstances of the two events differ throughout, from the persons present to the well itself, which fits two real occasions.