Because Shohei Ohtani isn't being consistently treated the same from platform to platform (eg Yahoo! Fantasy Baseball has two versions of Ohtani, and other platforms have one), there is no standardize convention for his treatment.
We have opted to assign only Ohtani as a Designated Hitter. Make sure you have the "Use Position" turned on for the DH to access these players.
An easy workaround for leagues that use two versions of Ohtani (DH & P)
Simply use another player as a representative of the SP version of Ohtani for your league.
For instance, find a player that won't likely be drafted, such as "Duffy, Danny (SP)" and inform your league that he will represent Ohtani the Pitcher. Then make sure to knowingly address this when inputting team rosters into your league management platform (eg Fantrax, ESPN, Yahoo, etc.)