"I need a name, not a job description. Doesn't anyone have any good, non-freaky girls names?"
As the sum of Chloe and Jewel, Joan possessed vast fighting skills, great physical strength, mastery of both Pattern and Logrus, and a mind of surpassing might.
In the attempt to repair Yig, in was decided that Chloe and Jewel should be merged using the shapeshifting abilities of Davros and Mitsune, on the grounds that an individual possessing great ties to both Order and Chaos, and the knowledge of how Yig functioned, would be needed to complete the Grand Conjunction. The resulting fusion was named Joan by Mitsune.
Joan was not completely like either of her parts, being somewhat more ready with her tongue than Chloe and somewhat more libertine and light of attitude than Jewel. She proceeded immediately to Yig, where she rewrote the regulation system from scratch and added allowances for the existance of the Pattern and Logrus into Yig's post-completion operational guidelines.
She also determined that the Heart of Yig had failed to form, and devised a method of creating it... which happened to be bearing it herself by growing it in her womb and giving birth to it. She drafted Asuka to provide the male half for this, and gave birth within a minute or two of Asuka's, ah, donation.
This done, she guided the Grand Conjunction to a successful conclusion and was carried from Yig, where after being told of the results of the battle she submitted to being separated back into Jewel and Chloe, and thus ceased to exist.
It is a matter for philosophy as to whether Joan is dead, simply in limbo until a future remerging, or was never enough of a separate entity to be capable of things like death. Chloe and Jewel seem to take the first view, and neither of them seems willing to ever undergo such a merger again except under the most dire of circumstances.
It is also unclear as to whether Joan should properly be counted as Chloe and Jewel, Chloe and Jewel's daughter, or something else entirely for the purposes of geneology. The question of what to count Yig is perhaps even more confusing. It will undoubtedly need to be addressed should any family member decide to marry the World-Tree, so that whether or not this would be incest can be determined.