if you change your signature or displayed name, the changes will only have an effect in threads that you post in after you make the change. So if you do not post in a forum after you change your name from, for example, buttmunch1 to beavereater36, then all your posts in that thread will remain as buttmunch1 posts. if you have posted a few times in a thread as buttmunch1 and you change your name and post in the thread again, all the posts in that thread get updated to be from beavereater36. This also applies to signatures in exactly the same way.
I am not sure if there's some kind of bot that goes round every now and again and updates the names on a weekly or monthly basis however as i have noticed that some of the new names appear in some old threads even when that person appears not to have posted there since the change.