The environment variable needs to be added to the tool making the permanent copy of the features. For example - if you have the AddJoin tool followed by the Copy Feature tool you would do the following: In Modelbuilder Right click on Copy Featuers > Environment > Make Variable > From Environment > Fields > Maintain Fully Qualified Field NamesThen you can click on the blue ‘Maintain Fully Qualified Field names’ variable and uncheck the option to maintain qualified field names (essentially making it ‘false’)Now the output will have 'Unqualified' field names.