There are plenty of examples of things which have a name put to them and after the passage of time and changes in circumstances the name no longer describes the thing accurately, but the name doesn't change.
That depends: Some cities e.g. in Italy have post-communist mayors, others have communist ex-mayors. When I want to tell friends a story from my married past, I never know whether to use "my ex-wife" or "my wife". At the time, she clearly was the latter...