You can’t run two copies of the smartthings app on one phone. You would have to sign out and sign in again with the other ID. But the other convenience option would be to use one of the dashboard apps, such as the free tier for sharptools. Since it runs in a browser, you can have it bookmarked for one account on the same phone that you have the smartthings app set up for the other ID. 
The following recent thread is a good discussion of dashboard options. Although the OP was looking for something for a wall panel, since these run in a browser, it’s the same thing for use on a phone.
FAQ: Sharptools , actiontiles or native ST app for your wall panel? (2020)