Options to manage how people contact you on Messenger
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You can't log out of an account on Messenger, but here are some things you can do to reduce notifications, make yourself unavailable or stop getting messages from certain people:
Turn off or adjust notification settings
Block someone's profile
Appear as inactive
Control your privacy
You can also switch Messenger accounts.
Note: If you think you've left yourself logged in on someone else's phone, you can end an active session from the Security and login settings in your Facebook app.