Here is how you can make your Spotify listening history private:
Step 1: A mobile Spotify session can be initiated by pressing the app's icon.
Step 2: The second action is to select the "home" symbol.
Step 3: You'll see the settings icon and tap it to open a menu of configurations.
Step 4: Select "Social" from the menu that appears.
Step 5: To begin a private session, tap the white button that appears next to it.