It’s very easy to turn FB Messenger's "Chat Heads" notifications off. Here’s how:
1 – Open the Facebook Messenger app on your phone.
2 – Tap the your profile photo at the top of the screen.
3 – Scroll down the list of options and toggle the “Chat Heads” setting to Off (it will turn gray).
That’s all there is to it. You shouldn’t be seeing any more Chat Head photos pop up on your phone’s screen.