At the time of the debates in the Hall of Servants, Latra Posae and Lews Therin were both equally respected to the point where there was a small number of people that were undecided - it was more like each having convinced 45% of the Aes Sedai, with 10% needed for a tie breaker. Latra Posae Decume's popularity exceeded that of Lews Therin's during his height, and she gained the name Shadar Nor (or the cutter of the Shadow) after Lews Therin had destroyed himself, his 100 Companions had gone insane and after she became the leader of the Aes Sedai and the forces of the Light during the Breaking.

She didn't gain her popularity for the Choedan Kal idea - she was already one of their leaders. She gained her lasting reputation after she took command of the Aes Sedai faction. This is why it is fitting to note that Saul was succeeded by David in this instance. There is actually a biblical saying: "Saul slayed his thousands, and David, his tens of thousands".