A script to detect a line break followed by the name of the character could, I assume, easily remove it and be rather easy to code. It wouldn't work if the name is typoed.
To prevent any unwanted message edits (the name might have been intended as something other than a signature, such as finishing your message with "You will regret having provoked John Bloe!")
However, a simple alternative would have the game tell you not to manually sign at the bottom of your message if it detects your name, while keeping it there. Much like how the game tells you not to share your civil work reports.
