John Gill Bible Commentary

And he called it Sheba,.... Which, according to Jerom, signifies "fulness", as if it had its name from the abundance of water in it; but rather it signifies an "oath", and was so called from the oath, which he and Abimelech had just took to one another; and these circumstances meeting together, the taking of the oath, and the account of the well: therefore the name of the city is Beersheba unto this day; that is, the well of the oath: it had been so called by Abraham an hundred years ago or more; but now upon this occasion it was renewed and confirmed, and so continued until the times of Moses, and many ages after.