Short answers, pulled from the story.
Dysnomia was discovered by Mike Brown and the Laser Guide Star Adaptive Optics team at the W. M. Keck Observatory in Hawaii. The discovery was made on the 10th of September 2005 using a newly commissioned laser guide star adaptive optics system.
Dysnomia comes from the Ancient Greek word meaning anarchy or lawlessness. In Greek mythology, Dysnomia is the daughter of Eris, the goddess of discord, which is why the name was chosen for Eris's moon.
Dysnomia has an estimated diameter of 615 kilometers, spanning between 24% and 29% of Eris's diameter. It is the second-largest known moon of a dwarf planet, after Pluto's moon Charon.
Dysnomia reflects only 5% of incoming visible light, giving it an albedo of 0.05 and a surface described as darker than coal. Eris in contrast has an albedo of 0.96. The contrast is consistent with Dysnomia having formed from material excavated by a large impact on Eris, bringing up darker subsurface material while Eris retained its bright methane or nitrogen frost.
Dysnomia orbits Eris at an average distance of approximately 37,300 kilometers and completes one orbit every 15.786 days, roughly half a month. Its orbit is nearly circular, with an eccentricity of 0.0062.
Before receiving its official name, Eris had been nicknamed Xena after the television character from Xena: Warrior Princess. Following that theme, the moon was nicknamed Gabrielle after Xena's sidekick. Both informal names were used by the discovery team until the official designations were announced in September 2006.