alyshadragonfriend's list "Greek Mythology Names 2" of 20 great name ideas: Hippodamia - Jocasta!

Greek Mythology Names 2

A list of the names of ancient Greek Gods, Goddesses, Heroes, Heroines, Monsters, etc., etc.

Hippodamia

Hippothoe

Homonoia

Horme

Hybris

Hygieia

Hylonome

Hypate

The name of a minor Greek goddess of healing.

Iaso

Ino was one of the Queens of Thebes who, after her death, became an immortal. Ino raised her nephew, Dionysus (son of Semele and Zeus), provoking the wrath of Hera. In desperation Ino threw herself into the sea and was thereafter venerated as Leucothea (The White Goddess).
 In Japanese, Ino means wild boar. Ino is most familiar in a Japanese context from Ino Yamanaka, a character in the Naruto anime.
 Despite being short and sweet, and bearing the fashionable "O" ending, Ino is one of the rarer Greek mythology names.

In mythology, Iphigenia was sacrificed by her father, Agamemnon -- a difficult legacy to pass on to a daughter, and only one reason the name is hardly ever used. 

Iphigenia

Sister of Antigone and daughter of Oedipus in Greek mythology, Ismene's name is unlikely to make it in modern times because of its teasability factor.  Ismay or Esme would be better bets.

Ismene

Ichnaea

Idyia

Ioke

Iphito

Ipotane

Iresione

Iynx

Jocasta is a mythological name fashionably used in England, but mostly ignored here. She was the mother of Oedipus, King of Thebes, whom he (oops) unwittingly married. If you can ignore that small error in judgment, you'll find an interesting and attractive J name that's neither overused nor terminally dated. 
 Jocasta is also a moon of Jupiter, and a Cloud Atlas character, playing in the film by Halle Berry.