Albert Barnes Commentary 1 Samuel 1:20

"And it came to pass, when the time was come about, that Hannah conceived, and bare a son; and she called his name Samuel, [saying], Because I have asked him of Jehovah." — 1 Samuel 1:20 (ASV)

Samuel - that is, heard of God, because he was given in answer to prayer. The names “Ishmael” and “Elishama” have the same etymology.