What is the sticky part of the pistil called?

The sticky part of the pistil is called the stigma.

The stigma is the pollen-receiving tip of a flower’s carpel, or of several fused carpels. Its surface is often sticky, hairy, or textured so that pollen grains adhere to it instead of falling away. Once compatible pollen lands there, it can germinate and produce a pollen tube.

That tube grows down through the style toward the ovary, carrying the male gametes to an ovule. Fertilization then produces a seed, while the ovary may develop into a fruit. The stigma, style, and ovary together are commonly described as the pistil, although botanical terminology can distinguish a single carpel from a pistil made of fused carpels.

A common mix-up is to call the entire central structure the stigma. The stigma is only the receptive tip; the style is the stalk beneath it, and the ovary is the enlarged basal region. Wind-pollinated flowers often have broad or feathery stigmas that provide extra surface area for catching airborne pollen.