The name is Ninna. The doubling matters. It is a diminutive of Yu’anan (Masoretic Yoh.anan) or one of the other names of the same meaning formed from el prefixed or suffixed to a form from the root h.et-nun-nun, such as Ânîl, Masoretic H.ani’el.
This does not exclude a connection with a Latin name Nonnus.
Bar Ninna, if it occurred, would mean son of Ninna.