In the prologue to Winter's Heart, the "Black Ajah Hunters", including Pevara force Talene to re-swear the three oaths.
Talene was in the same heart as Galina and hers is one of the names that is revealed, we get this information in the Crossroads of Twilight prologue in Yukiri's point of view. Encylopedia Wot, surmises it here as:
Talene exposed the other two of her circle, Galina Casban and Temaile
Kinderode, and her outside contact Atuan.
There's a more detailed summary of the scene on the Wheel of Time re-read.
Here's the quote from the book:
Now Talene was tethered tighter than Meidani, closely guarded even if
she did appear to walk free - how to keep a Sitter prisoner without
anyone noticing had been beyond even Saerin - and she was pathetically
eager to offer up every scrap she knew or even suspected in hope it
might save her life, not that she had any choice. Hardly an object of
fear. As for the rest. . . .Pevara had tried to maintain that Talene
must be wrong about Galina Casban, and went into a rage that lasted a
full day when she finally was convinced that her Red sister was really
Crossroads of Twilight, Prologue, Glimmers of the Pattern