First off, naming conventions! Yisun's name would be different, as Drahns do not have Mongolian-inspired named, nor do they seem to have tribes. Her last name, then, would be impossible to tell, but her first First name would be Sunwren (pronounced soon-ren). (First half, "Sun-", deriving from her original name and following the one-syllable surname convention; Second half, "-wren", because out of all the ones we know, it sounded the cutest.)
Sunwren's backstory would be a fairly common one: the small group of survivors she was a part of would have been attacked by sin eaters, wiping all of them but herself out. I figure that, same as Yisun, she was saved by Source!Aja, then traveled with him to the Crystarium, where they parted ways. There, she eventually trained at Spagyrics before leaving to volunteer at the Inn at Journey's Head, taking care of those afflicted by the light. She does this partly due to fear, since her albinism means that it would be visually difficult to tell were she to become afflicted.
Bonus super-sad Thought Experiment of the day: Sunwren and Source!Aja's reunion comes too late, as by the time he seeks her out she has become infected by the light and no longer recognizes him. u-u)