On the etymological references to Saul in 1 Samuel 1, see Brettler, Marc. “The Composition of 1 Samuel 1-2.” Journal of Biblical Literature, vol. 116, no. 4, 1997, p. 602. "This half-verse [1:28a], which is so rich in the root [shaal], can only with great imaginative effort be made into an etymology of Samuel rather than Saul."
For bibliographical information about scholarly arguments for 1 Samuel 1 originally being about Samuel, see Brettler, Marc. “The Composition of 1 Samuel 1-2.” Journal of Biblical Literature, vol. 116, no. 4, 1997, p. 602.