This is Ezri Dax… She is a Trill. Some trill host symbiotes. The symbiotes live longer than their hosts. During hosting memories and personalities blend, and the symbiote will carry that blending into the next host.

Her symbiote is named Dax and was previously hosted by both another female, Jadzia, and a male Curzon, and several others.

Jazdia Dax was the name of Jadzia hosting Dax. Curzon Dax was the name of Curzon hosting Dax.