Charles Ellicott Commentary Genesis 21:3

"And Abraham called the name of his son that was born unto him, whom Sarah bare to him, Isaac." — Genesis 21:3 (ASV)

Abraham called the name of his son. — Attention has been called to the fact that we have here two things contrary to later usage: first, the father names the child, and not the mother; and secondly, he names him at his birth, instead of waiting until his circumcision. It might be enough to answer that the child was really named by God (Genesis 17:19), and that Abraham only acknowledges that the son born was the promised Isaac. However, as we have seen before, there was still no settled rule regarding either of these points.

Isaac. — This name not only recorded the fact of the laughter of the father (Genesis 17:17) and of the mother (Genesis 18:12), but was a standing memorial that Isaac’s birth was contrary to nature, and that the promise of it provoked ridicule even from his parents.