Posts themselves will stay linked but where people quoted you will break, because their post contains the old name so where the system would usually add your avatar and a link to your profile, it can no longer do that, so they look like this example from when Halastjarna changed her screenname from Anastasiya.
It doesn’t break the quote, just removes the av & link. 
For people searching the forum in future for this topic, @HermesHorse is correct, search in your profile, I’m not sure what you can change at different levels of membership (these progress via post count and time active on the forum) but if in doubt just PM me, send the exact spelling complete with capitalisation you require because I’ll paste it in exactly as given.