You can rename an account and in the list of accounts, and all various views (new messages notification, etc.) the new name will appear. But in case of the widget, - it is essentially a name of the widget pointing to that account, and it will not change when you are renaming the account to which that widget is linked.
(I am not using widgets, so, something with respect to the widget behavior might have changed since the original discussion in this old (2012!) thread.)