Saul's royal court governed a country of many millions of people which would have required both a central and distributed bureaucracy or reasonable size. David, when he began his service as a court musician (1 Sam 16:19-23), would have been a very minor court official with the most perfunctory (brief with minimal details) introduction to Saul. This would have been made worse by Saul's rapidly developing mental illness.
In 1 Sam 17 we have a barely noticed court musician suddenly being revealed as a significant warrior with astonishing audacity. Correspondingly, Saul now needs to know MUCH more about this lad and his origin - I am sure that the conversation between David and Abner was much longer and more detailed than the single sentence recorded in 1 Sam 17:58, precisely as suggested in 1 Sam 18:1, 2.
After David had finished speaking with Saul, the souls of Jonathan and David were knit together, and Jonathan loved him as himself. And from that day Saul kept David with him and did not let him return to his father’s house.
This also suggests that David, up to this time, was only part-time in the royal court, but themthen became a full-tiletime courtesan in the service of Saul.
It is also possible that Saul's mental illness contributed to his poor memory of the hitherto minor courtesan and wanted a fuller introduction to what would obviously be a very useful person to Saul.
Benson observes this:
1 Samuel 17:55. Whose son is this youth? — It may, at first sight, appear strange that Saul should be represented here as not knowing who David was, when we have a relation in the foregoing chapter of his sending for him to court, being highly pleased with his behaviour, and much delighted with his music, making him his armour-bearer, and sending to his father Jesse to ask his leave for his continuance at court. But it may be observed that Saul, in this place, does not express an entire ignorance of David, but only inquires whose son he was — A question of the more consequence to him, as he had promised his daughter in marriage to the conqueror of Goliath. Either Saul had never before made any inquiry about his parentage, or both he and Abner had forgotten whence he was. And this might very easily happen to a king and a general of an army, who daily see and have to do with so many different faces, and who pay so little regard to things of this sort. Nay, if Saul had entirely forgotten David, it would not have been strange, considering that he had been but little with him, had some time ago been dismissed from the court, and was returned home, where he had remained at least a year or two, during which time Saul had not seen him. Besides, the distemper of Saul’s mind might make him forgetful, and David might now be much changed, both in his countenance and in his habit. Abner said, I cannot tell — Abner’s employment was generally in the camp, when David was at the court; and when Abner was there he probably took little notice of a youth so much inferior to him as David was.