John Gill Commentary Genesis 16:15

"And Hagar bare Abram a son: and Abram called the name of his son, whom Hagar bare, Ishmael." — Genesis 16:15 (ASV)

And Hagar bore Abram a son Being returned to his house, and received by him, and reconciled to Sarai, she brought forth a son to Abram, according to the prediction of the angel:

and Abram called his son's name, which Hagar bore, Ishmael ; and this name Jarchi suggests he gave by the inspiration of the Holy Spirit that dwelt in him: but it is highly reasonable to suppose, that Hagar upon her return reported to Abram the whole of the conversation she had with the angel; therefore Abram believing what she said, in obedience to the order and command of the angel, gave him this name.