Per its title, Psalm 52 was written after which man told Saul where David had gone?

Answer: Doeg the Edomite

It was written after Doeg the Edomite told Saul, "David has gone to the house of Ahimelech."

“For the choirmaster. A Maskil of David. After Doeg the Edomite went to Saul and told him, “David has gone to the house of Ahimelech.” Why do you boast of evil, O mighty man? The loving devotion of God endures all day long.”— Psalm 52:1 (BSB)