I changed my username on the University profile page, as the default was simply wrong (I’m called “Björn” or “Bjoern”, but not “Bjorn”).
I searched how to change the username in the forum here and found Changing username / email address which suggested to log out and back in.
Actually trying to log out was enough.
I was still logged in, but now with the new username.
While I find it pretty strange that there is a logout button that does not work as you are automatically logged back in, the existing mentions were not updated.
If you for example look at Are Final Exam answers editable?, I was addressed in the answer with the old username. This mention is still like it was before, just that it now is not clear that I am meant and if you click on it, you get a 404 error message, as the profile page with the old username does not exist anymore of course.