There is no way to turn off the "Player name is a ___" message that appears above the hotbar when using /identity test. There should be a config option to turn it off, or make it print the result to the chat or console instead of the screen.

I'm making a datapack that relies on the identity mod, and the test command is very important, but when you are constantly testing to see if the player is a certain morph you constantly have that message above the hotbar, which makes it extremely irritating.