John Gill Commentary Genesis 26:33

"And he called it Shibah. Therefore the name of the city is Beer-sheba unto this day." — Genesis 26:33 (ASV)

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 taken 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.