I don't personally know anyone named Oona but it's a very nice name. Some good nicknames are Oon, Oono, Moon, and O. I guarantee the person you're using these nicknames on will be so thankful. OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOna.
I once knew an Oona, years ago. We're American, but she had an uncommon Irish surname and her roots were very (East Coast) Irish, so her name didn't look odd on paper. And to be honest, Oona wasn't odd to say in real life, despite it being so unlike the usual names in this country. It slowly grew on me.Only this spelling, though. Una looks too much like Spanish "uno," and Oonagh just has too many letters.