havelock

n. cloth addition on a hat that provides additional protection from the sun (especially to the neck)

The name Havelock originated as an English surname and means "sea war." The surname has since also given rise to various place names and is often also used as a first (given) name and occasionally as a middle name.
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Noun
1. a cloth covering for a service cap with a flap extending over the back of the neck to protect the neck from direct rays of the sun
(hypernym) cloth covering

(n.)
A light cloth covering for the head and neck, used by soldiers as a protection from sunstroke.
  

The cloth that hangs from the back of a hat to protect the wearer's neck