Ahh yes, the surname Ong I think also means 'young' and is perhaps most likely of Old Norse origin, from Old Norse 'ungr'. I am coming to conclude that the surname Own/Onn most likely derived from 'young', also as English and Scottish surnames Young, Yong, Younge, Youngs, and I think the Norfolk surnames Younge and Ong are of Old Norse origin of the same meaning. But are the Owns/Onns of English, Scottish, or Scandinavian origin? I think most likely either Scandinavian or Scottish. I am leaning more towards of Scottish heritage, because of the connection that both the surnames Ogg and Owns/Onn are mostly found in regions Northern Lincolnshire and Northeastern Lincolnshire, and that perhaps the Ogg of Lincolnshire are most likely Scottish. The surname Ong is from East Anglia, and they are rare in Lincolnshire, but overall, I'm not sure.
Another theory I came across was that then name Onn could derived from Welsh 'onn' meaning ash trees, but I think perhaps not likely for the origin of the Own/Onn of Lincolnshire.