Ah. Yeah. I just played around a little. I don't see an option to sign out in the Messenger app and when I signed out of the main fb app, I was still signed in to Messenger.
You could go into settings and clear the data on the messenger app, but you would have to do that every time and if you're still logged in to the main facebook app, I believe it gives you the option to continue as yourself when you open messenger and doesn't require a password.