Oedipus. Homer called her Epicaste (which name see). The Greek form of her name is Iocaste, and this is usually derived from io, 'moon' (see Io) and either cazo, 'to adorn' or caio, 'to blaze' (as perhaps in the name of Castor). This means that she was 'adorning moon' or 'shining moon'.
But this seems too agreeable a name for her, unless it is intended propitiously. If we regard the initial 'io' as a cry of woe (io could be a cry of both joy and sorrow), then we can propose the more suitable 'woe-adorned' for her. After all, her troubles began when an oracle warned her first husband Laïus that any son she bore him would kill him. (This was how Oedipus got his swollen foot - see his name.) Then, after unknowingly marrying her son, Jocasta was so shocked that she took her own life (in Homer's account). Furthermore, at any rate according to Homer, her name was changed from Epicaste to Jocasta specifically to indicate a change in her fate.