John Calvin Commentary Genesis 16:14

"Wherefore the well was called Beer-lahai-roi; behold, it is between Kadesh and Bered." — Genesis 16:14 (ASV)

Wherefore the well was called I subscribe to the opinion of those who interpret the word יקרא (yekra) indefinitely, which is common enough in the Hebrew language. So that the meaning may be clearer, it can be rendered in the passive voice, as ‘the well was called.’ Yet I think this common name originated with Hagar, who, not content with one simple confession, wished that the mercy of God should be attested in the future; and therefore she passed on her testimony, as if from hand to hand.

From this we infer how useful it is that those who do not willingly humble themselves should be subdued by hardships. Hagar, who had always been wild and rebellious, and who had, finally, entirely shaken off the yoke, now, when the hardness of her heart was broken by afflictions, appears to be an entirely different person.

She was not, however, brought to order by hardships alone; but a heavenly vision was also added, which thoroughly arrested her. And the same thing is necessary for us; namely, that God, while chastising us with His hand, should also bring us to submissive meekness by His Spirit.

Some among the Hebrews say that the name of the well was given to it as a testimony of a twofold favor, because Ishmael was saved from death, and God showed regard for Hagar, his mother. But they foolishly mutilate things joined together: for Hagar wished to testify that she had been favorably regarded by Him who is the Living God, or the Author of life.