In "Through the Looking Glass" (S3E19 of DS9), mirror O'Brien kidnaps Benjamin Sisko from the primary universe to temporarily replace the dead mirror Sisko who is/was the leader of the Terran rebellion. Upon reaching the rebellion's base in the Badlands, we meet mirror Jadzia for the first time. Later, in a meeting of the rebels, Sisko refers to her as Dax, which doesn't surprise or confuse anyone - but why would she be joined with the Dax symbiont?
We know that once joined, the name of the symbiont replaces the family name of the host (as Ezri Tigan becomes Ezri Dax when she is joined to Dax after Jadzia is killed). Therefore Jadzia would only become Jadzia Dax after having joined with Dax, so if she isn't joined she should still be using her original name.
In talking with Sisko, she makes clear that she was a slave on Terok Nor, so she's unlikely to have had the opportunity to be joined with Dax - indeed it seems unlikely that the Alliance would permit any Trill to become joined at all if they are all slaves.