It's easy to switch between your different dogs in the app. Simply click the "more" menu, and in the top right-hand corner of the pop-up menu click the "switch dog" icon. You can then access any of your other dogs' information.
Rest assured, should there be an important event with one of your other dogs, you will receive either a push notification or an in-app message about that dog (i.e. a change in location state to/from "Away").
Please make sure to enable permissions in your phone's settings.