Why does the enzyme pepsin (present in the stamch) denature in the intestine?

The enzyme denatures due to the alkaline environment of the intestine.

Correct, Pepsin denatures in the small intestine (duodenum) due to the higher pH (more basic or alkaline), and also the lack of HCl (neutralized by the base bicarbonate in the duodenum), which is a potent activator of pepsin in the stomach.