I think what I would do is create a second TestComplete project for the testing the new version.
For the tests that are the same in both versions, use Add Existing to put them in the second project. This will create a pointer back to the original test, so even if you edit it in the new project, it's the same file.
For the name mapping, make a copy of the original name mapping file and use Add New to put it in the second project. Edit this one to match your changes for the new version.
For tests that will be unique to either version, use Add New in the appropriate project.