I’m actually Greek and I asked my Ancient Greek teacher the etymology of the name and she said it comes from the Greek ίον meaning violet and κάζω meaning decorate. After some searching in Greek this etymology can be found in many Greek name sites and dictionaries.
So I did a lot of digging for this, because I heard somewhere this name means "shining moon" but I don't like taking things at face value.I broke the name up into Io (the Greek form of Jo) and casta. I recognized Io from the Io that Zeus fell in love with, and I finally found Martin Bernal's book Black Athena, where he mentions it may be connected to jꜥḥ, or Iah, who was a god of the moon. The word jꜥḥ literally means moon in Egyptian, so the first part of Jocasta's name we can assume shares that meaning.-casta was a lot easier. It already sounds like "cast" like "to cast light", but I did check and it may be related to κέκασμαι (kékasmai) meaning literally "to shine." It relates to names like Castor and Cassandra. So her name really does mean "shining moon," or something along the lines of "moonlight."