I've never actually done it. But there is a permission, which I've always seen denied by default, to allow the users to change their username. I expect that once the users have been allowed to change their username, yes it would change their username when viewing historic posts. Because it's the numeric user ID, and not the user name, which is tracked as the author of the post.
One place which probably will get "left behind" is the old "dumb quotes" references to their old name, since changing the username for a particular user ID isn't going to affect anything about an old "
[quote="Activ8r"]" reference in a message. The new "smart quotes" references (e.g. "
[quote=Activ8r post_id=15278861 time=1561435333 user_id=1790456]") at least have the opportunity to reflect the new name, since they track the user ID in addition to the name. But again, I've never actually renamed a user account to confirm whether it does or it does not.
edit: The permission I'm referring to is "Can change username" in the "Profile" tab of the user permissions.