There is confusion as to why King Saul asked who David's father was in 1 Samuel 17 because the preceding 1 Samuel 16 chapter already recounts the story of how King Saul came know and meet David.
However, Is it possible that King Saul merely asks who David's father was in 1 Samuel 17 for rhetorical effect in response to seeing how a young shepherd boy like David killed a giant named Goliath?
1 Samuel 16:17-22 New American Standard Bible 1995
17 So Saul said to his servants, “Provide for me now a man who can play well and bring him to me.” 18 Then one of the young men said, “Behold, I have seen a son of Jesse the Bethlehemite who is a skillful musician, a mighty man of valor, a warrior, one prudent in speech, and a handsome man; and the Lord is with him.” 19 So Saul sent messengers to Jesse and said, “Send me your son David who is with the flock.” 20 Jesse took a donkey loaded with bread and a jug of wine and a young goat, and sent them to Saul by David his son. 21 Then David came to Saul and [a]attended him; and [b]Saul loved him greatly, and he became his armor bearer. 22 Saul sent to Jesse, saying, “Let David now stand before me, for he has found favor in my sight.”
1 Samuel 17:55-58
New American Standard Bible 1995
55 Now when Saul saw David going out against the Philistine, he said to Abner the commander of the army, “Abner, whose son is this young man?” And Abner said, “By your life, O king, I do not know.” 56 The king said, “You inquire whose son the youth is.” 57 So when David returned from killing the Philistine, Abner took him and brought him before Saul with the Philistine’s head in his hand. 58 Saul said to him, “Whose son are you, young man?” And David answered, “I am the son of your servant Jesse the Bethlehemite.”
17:55-58 The Westminster Leningrad Codex
55 וְכִרְא֨וֹת שָׁא֜וּל אֶת־דָּוִ֗ד יֹצֵא֙ לִקְרַ֣את הַפְּלִשְׁתִּ֔י אָמַ֗ר אֶל־אַבְנֵר֙ שַׂ֣ר הַצָּבָ֔א בֶּן־מִי־זֶ֥ה הַנַּ֖עַר אַבְנֵ֑ר וַיֹּ֣אמֶר אַבְנֵ֔ר חֵֽי־נַפְשְׁךָ֥ הַמֶּ֖לֶךְ אִם־יָדָֽעְתִּי׃
56 וַיֹּ֖אמֶר הַמֶּ֑לֶךְ שְׁאַ֣ל אַתָּ֔ה בֶּן־מִי־זֶ֖ה הָעָֽלֶם׃ ס
57 וּכְשׁ֣וּב דָּוִ֗ד מֵֽהַכּוֹת֙ אֶת־הַפְּלִשְׁתִּ֔י וַיִּקַּ֤ח אֹתוֹ֙ אַבְנֵ֔ר וַיְבִאֵ֖הוּ לִפְנֵ֣י שָׁא֑וּל וְרֹ֥אשׁ הַפְּלִשְׁתִּ֖י בְּיָדֽוֹ׃
58 וַיֹּ֤אמֶר אֵלָיו֙ שָׁא֔וּל בֶּן־מִ֥י אַתָּ֖ה הַנָּ֑עַר וַיֹּ֣אמֶר דָּוִ֔ד בֶּֽן־עַבְדְּךָ֥ יִשַׁ֖י בֵּ֥ית הַלַּחְמִֽי׃