You can create multiple configuration of the NameMapping under the same project.
Lets say your project is running in multiple languages and all the objects are having same properties for that(only text/captions are change) in this case. instead of creating new project I think it would be better to create New Configuration of NameMapping and load it at run time. as per the requirement.
To create multiple Name Mapping configuration -
1- Name Mapping editor
2- Configuration Manager
3- Click on "Copy as New" button
4- Enter configuration Name
5- click on Ok and close -configuration manager
Now you can modify/update object without hampering your original NameMapping.