I chose this name because of the classical mythology surrounding Medea.
In Greek mythology, Medea is an evil witch. She appears a few different times, but mainly in the myth of Jason, or the myth about the Golden Fleece.
She began as a divinity, who, of all things, was not evil, but very benevolent, worshipped in Corinth and Thessaly. She was thought to have great knowledge of medicine. Over time, she became a female sorcerer, and then, Jason's rejected woman, finally becoming a mythological serial killer, killing many people; the most vehement kills being her younger brother and her daughters (fathered by Jason).
I used to love that myth; it was like a fairy tale, where the good, handsome hero goes across the sea, meets and falls in love with the princess. She is a very powerful princess, (oh so rare in myth and fairy tale!) , who saves his live in the trials her father sets for him, as well as stealing the fleece for him. The myth suggests that the gods who liked Jason (Hera and Athene) convinced Aphrodite to make her fall in love with him, thereby giving him the ability to attain the fleece.
And then, suddenly, Medea, the powerful woman who could do so much else with her sorcery, has to resort to killing her little brother and cutting him up into little pieces to drop into the sea and distract her father from chasing them down.
In the latter versions of this myth (once it had been influenced by the myths about Odysseus' journey home) they get lost, and time and time again, Medea somehow saves her incompetant hero, usually by killing the beast who attacks them for them. One version, her father catches up with them and demands that she is returned, so long as she is still a virgin. They hurry up, get married and then fuck so that she is not returned (because no one in classical myth would ever have sex before marriage!). Maidenhead no longer in tact, Medea is now free of her father. This is about the only time Jason rescues Medea (and what a rescue that one is...).
Finally, they arrive back in Athens and she helps Jason once again, by removing his usurping Uncle from the throne so that he may take his rightful place as King. They have a few daughters, and then Jason wants to get married again for political reasons. Medea goes into a rage and sends his bride a cloak that burns her to death the moment she puts it on. Then she murders her daughters and runs away from Athens in her chariot, pulled by dragons. The gods, by the way, feel that she as somewhat justified, since polygamy wasn't considered "the thing to do", as well as the fact that Jason was certainly one of the most demasculated Greek heroes, and drove Jason mad.
Even in the course of the myth she goes through this huge transition, from saving Jason's live to motive-less killings (such as her daughters, even if their father was Jason).
She is, of course, not the only powerful female deity or god who has gone through a transition from "divine" to "mere" over the ages. In classical mythology, many of the princesses, queens and such stem from what were once gods. Polyxena, for one, was once a god of the underworld, and then reduced to a Trojan princess who Achilles wanted (and his son sacrificed at the end of the Trojan war to appease Achilles). Helen was another example of this, being first a fertility god, then a pretty face for the big boys to fight over. This happened to male deities too. In Christianity also, the importance of Christ's mother fluctuates, depending on who you're talking to.
But Medea has always stood out to me. The particularly gruesome features of her crimes aside, (such as kidnapping her kid brother to cut him up), all she ever does is continuously rescue her helpless hero from dangers that would otherwise kill him. Jason is just about the only Greek hero who seems about as helpless as the generic fairy tale princess; constantly getting into patches of trouble, then needing a rescuer. So what if Medea doesn't use a sword, but instead brains and sorcery! It's the same formula as the male hero slaughtering whatever creature the pretty girl has gotten herself caught up with. The only difference is that when Medea does it, she dishonours her pal... because he loses boy points.
Myths, of course, aren't really set in stone; it should never be stated that there is a "correct" version of any myth, fable or fairy tale, as they are all oral entites, and meant to be retold, and changed as the tellers like. It's a sad thing that today we all want the concrete and "real" version of things, when there never is a concrete or real version of any story. They were always meant to relay a message, and I don't mean that each story needs a concrete moral.
In my retelling of the myth of Medea, she is not, by any stretch of the imagination, evil. She also is not so simplistic that she is just good. Dualism (including the dualism we set up between male and female) is an oversimplification of the world around us. Medea, for me, is someone who worked very hard to protect someone she felt very strongly for. For me, she has always been one of the few women in classical mythology who is consitently strong, who consistently works on the same level, or higher, as her male counterparts. Even when I was a little girl reading books about Greek myths for children, she stood out to me. She was filled with the potential (often ignored) for complexity and nuance.
This is why Medea is so important to me as not only a character, but an idea.