When the Greeks added the th to Ka creating Kath they also focused on the idea that Heket and Hekate were pure (they were (or she was) worshiped by Egyptians and Greeks). The meaning of Kath became purity. At one point most name references said that Kath meant purity like the sun sparkling on the waves. I don't know whether this is when the Catholic church stepped in as a religion and claimed Cath as a prefix. I've also been told that in Ireland Kathleen developed another meaning. Kath=Kathrine and Leen = Little, so Kathleen means little Kate.