It is known as "Bonnet Rouge" (French) or red hat (English). The Liberty Cap dates back to ancient Roman and Greek times as part of a ceremony of freedom for slaves and is known as the "Phrygian hat."
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It is not of anyone in particular, but it is the personification of Liberty. Since Liberty wears a winged cap, it is commonly thought to be the god Mercury and so its common name is a Mercury dime.
The liberty pole was a symbol of revolutionary solidarity in the time of the American and French revolutions. An ensign or symbolic soft cap would be placed atop a pole, or in some cases a tree, to show support for the rebellion.
These are normally called Mercury dimes because the winged cap worn by Miss Liberty looks a lot like the cap worn by the god Mercury. See the related link for values
While that's the technically correct name for this coin, they're almost universally known as "Mercury" dimes because of the winged cap worn by Miss Liberty. There's more information at the Related Question.
That's a Barber or Liberty head dime. Face shot of Liberty w/cap & wreath designed by Barber.