The FB app allows people to register (and login) from Facebook, choosing a different name if they wish.
Once they have logged in (registered) via Facebook, they have a user record in the database, the same as any other member.
They don't have a password initially but they can request that one be generated and emailed to them (in the account section), or this will automatically be done if they disassociate their FB account.
They can then log in using the user name or email address and password, like any other member.