The hairstyle in which hair is tied back at the nape of the neck is a ponytail.
A ponytail is made by gathering some, most, or all of the hair at the back of the head and securing it with a tie, clip, or similar accessory. The loose hair hangs freely from the fastening point, and the nape of the neck is one of the most traditional places to position it. Ponytails can also be worn high on the crown, at the side, or low near the neck.
The style takes its name from the resemblance between the hanging hair and a pony’s tail. Artistic evidence suggests that versions of the ponytail appeared in Ancient Greece, with similar styles also represented in Egyptian and Roman art. In modern Western culture, the style became especially associated with girls and young women in the mid-20th century.
A chignon or bun is generally coiled or pinned into a compact shape, while a braid interlaces strands. Those styles may be worn at the nape, but they are not ponytails unless the hair remains gathered and hanging freely.