In American the meaning of the name Ona is: Graceful. Irish Meaning: The name Ona is an Irish baby name. In Irish the meaning of the name Ona is: One. Also a Lamb; together. Latin Meaning: The name Ona is a Latin baby name.In Latin the meaning of the name Ona is: Only child; also can be a One.n American the meaning of the name Ona is: Graceful. Irish Meaning: The name Ona is an Irish baby name. In Irish the meaning of the name Ona is: One. Also a Lamb; together. Latin Meaning: The name Ona is a Latin baby name.