Report - require unique names

I noticed that for a search, the system doesn't allow it to be saved with the same name. But for a report, even if permission is set to Edit (instead of Full), when you customize someone else's report, you won't be able to save directly, but you can still save as and using the exact same name. This creates a lot of confusions in the system where we search a report and multiple reports with the same name show up. Is there any way to prevent it? I understand when creating the same name, the system pops a warning, but