The first time you hear about her, she is refferd to as Lord Zash. So I assume that's either her firstname or surname. Later in the story line, she becomes a Darth. Usually when one receives his/her Darth title, s/he gets a new name. Which (most of the time) means something too.
For example Dart Vader, frominvader. Darth Sidious, from insidious. You also have this in-game. Darth Decimus, because he decimates the enemy numbers (?), Darth Ravage because....well, that one is pretty obvious
Anyways, she remains Darth Zash and I wonder why. I believe it was Thanaton who gave her her title. Since she needs to come to his office, and when you return to her she is Darth Zash. Perhaps Thanaton was mad because of the Skotia incident and decided to troll her? Then he better gave her a really humiliating name