Update notifications content after they’re sent

Let's say that I have a notification system embedded in a forum. Whenever someone creates a thread, we'll send notifications about this new thread to some users. But, if it happens to the thread owner update the thread title, should I go ahead and update all notifications to all users as well?

Another question is, say that my notification will read like: "User Foo Bar replied your comment 1 minute ago". I'm also wondering if I should update all notifications if Foo Bar changes its name to Bar Baz.

Doesn't look like consistent, but I have the feeling that notifications should be immutable and never change once they're sent.

What are your thoughts?