Cordelia Misericordia was a hag living in the 14th century. She represented hags at a summit of the Wizard’s Council.
Cordelia is a feminine given name. It was borne by the tragic heroine of Shakespeare's King Lear (1606), a character based on the legendary queen Cordeilla. The name is of uncertain origin. It is popularly associated with Latin cor (genitive cordis) "heart", and has also been linked with the Welsh name Creiddylad, allegedly meaning "jewel of the sea", but it may derive from the French coeur de lion "heart of a lion." (Wikipedia)
Misericordia is the Latin for "mercy", derived from misericors, "merciful", which is in turn derived from misereri, "to pity", and cor, "heart". In Medieval Latin, the word "misericordia" denoted various merciful things, and these senses were borrowed into English. (Wikipedia)
Interesting that although the name has a negative connotation, connected visually with the word "misery," the actual meaning suggests empathy and mercy. Hags are looked at in a negative light and misunderstood in the Harry Potter universe, just as the name meaning can be misunderstood.