Repro steps:
1. Open the attached project
2. In the project window click on the Enemy prefab and click again, to edit the name - nothing happens, can't edit the name this way
3. Having the prefab still selected, in the inspector window change the name of the prefab and press enter

Result: the name of the prefab visible in the project window stayed unchanged but it's changed in the inspector view (see the attached print screen)
After the project is reopen, the new name is saved