You can change a persons name in Facebook Messenger, but it only shows on your side. Not theirs. To show on their side they have to log in to their own Facebook account and change it.
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My friend changed her last name and it is showing up correctly on all my devices, except for my iphone 6 and my ipad Facebook messenger. That sidebar still remains as her former name. Is there a way I can change that on my devices? She has changed her last name everywhere she possibly can and it still won't change in my messenger. People without apple products have had no problem with the change...it has automatically changed for them.