It's actually very simple to change a GameObject's name. I believe you're trying harder than you are supposed to. Go to your Hierarchy window, and select the object you want to rename by clicking on it. It will turn blue. Click it again and you will be able to change the name of it, no script required. Be careful though, do not double-click the object(meaning do not click the object twice too fast). This will do something completely different.
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