Hi, when you say "back end" are you meaning as done by your org. or have you done something yourself with your personal account? Easiest way to see if the change has been processed is to sign in on the web app https://teams.microsoft.com using InPrivate Mode (the latter only for not using any cached files).
This process can take some time depending on environment but usually a manual sign out quickens the sync.
if what Christian wrote doesn't help, I would argue that it's a matter of time. With our users, such a change sometimes takes up to 24 hours until it is synchronized everywhere (Teams Desktop Client, WebClient,...).
"back end" meaning I have logged into my microsoft account via my web browser and changed my change on my microsoft account and every time I log in to that it does show my name change but when I go to team either via my desktop app or via the web https://teams.microsoft.com it doesn't show my name change. And if I try to go to "Manage Account" it asks me to sign in to Microsoft again but when I put my email address in it, it then comes up with a sign in error "xxxxx.com.au isn't in our system". "make sure you typed it correctly".
But yet I can happily sign into my microsoft account if not via teams.