Why did Absalom set up a pillar named after himself in the King's Valley?

Answer: He had no son to carry his name

Absalom said, "I have no son to preserve the memory of my name," so he named the pillar after himself: Absalom's Monument.

“During his lifetime, Absalom had set up for himself a pillar in the King’s Valley, for he had said, “I have no son to preserve the memory of my name.” So he gave the pillar his name, and to this day it is called Absalom’s Monument.”— 2 Samuel 18:18 (BSB)