I am using the Google Play Games app for creating recordings. During recording of a game play, there is a console logo which gets recorded, too, as well as notifications.
How to avoid that?
The console logo when using Google Play Games appears when you are only recording the screen and not yourself. You can't remove it. It's either the console logo or your face (unless you block the front camera, then it will be a black circle that will be shown on your videos).
Your alternative is to record games using the screen recorder that comes installed with your phone (check if yours has one) or download a screen recorder apps from Play Store.