They call the sport “curling” because the stone literally curls —it travels in a gentle curve across the ice instead of in a straight line.

Quick Scoop

When a player releases the granite stone, they give it a slight rotation, known as the “turn.”
That spin, combined with the textured “pebble” on the ice, makes the stone’s path curve as it slides.
Early Scottish players noticed this distinctive curving motion and described it with the verb “to curl,” which led to the name “curling.”

The sport picked up another nickname, “the roaring game,” from the rumbling sound the stones make as they travel over the pebbled ice, but the official name stuck to the visual: stones that curl.

TL;DR: It’s called curling because the spinning stone doesn’t go straight—it curls along a curved path down the ice.

Information gathered from public forums or data available on the internet and portrayed here.