From the experts:
Oona is a name made famous by Eugene O'Neill's daughter, who became Charlie Chaplin's wife. One of the original Oona's granddaughters was named after her, and is now an actress famous in her own right for playing Talisa of Volantis in HBO's "Game of Thrones." The double-o beginning gives their name a lot of oomph.
In Irish legend, Una/Oona was a daughter of a king of Lochlainn. The name was very popular in Ireland in the Middle Ages, and is currently seeing a comeback--also spelled Oonagh.