The best champions not in lane to counter Ornn include Zeri, Aphelios, and Jinx. These champions are all great at countering Ornn with win rates over 56%. Even if these Ornn counter picks are not used opposite your position, it's not a good idea to take him into these matchups. They will likely crush Ornn.
Conversely, if the other team choses either Tahm Kench or Ziggs, you should seriously think about choosing him, as he easily crushes these champions with win rates over 54% against each ofthem.