General terms:
* Hair tie
* Scrunchie (a type of hair tie made of fabric)
* Hair elastic
* Hair band (can also refer to a headband)
* Hair accessory
Specific types:
* Ponytail holder
* Bun holder
* Hair clip
* Hair barrette
* Headband
* Hair comb
* Bobby pin
The best term to use will depend on the specific type of hair holder you are referring to.