Are names, where diacritical marks are lacking, exonyms? No
Are names, where the articles are lacking, to be considered as exonyms? No
Are names, where case endings are lacking or added, exonyms? No
Are names, whose generic parts have been translated, to be considered as exonyms? Not sure.
For instance Aigaion Pelagos Aigaion Sea
Are exonyms a problem? Definitely!
Both nationally and internationally.
Why?
Because of the confusion they bring.