If you change your name on Facebook and block someone?

[pri✍]

No, I don't think by doing that you achieve what you want, ie. change the name on the existing message on their end. Because what ever name you changed to (while it reduces your limited chance to change your name by 2, ie change name to something else, then change back to your original name), even for them it's a dead link because you block them; to FB, it's a live link, and FB will link it/alter it to the current name you use.

It only be changed to Facebook User automatically by FB if you deactive yourself. But once you reactivate your deactive account, your name will appear again. The message itself still intact in their Inbox. I don't know if that's true if you delete yourself, can't tried that to proof it.