I played around with it for a little while before finding the article above. I found that I could create the behaviour you described, but equally I could rename instances of the prefabs which were in the scene, the Inspector would display the renamed instance correctly but in the Project view it remained the same. I could save the scene/project and these didn’t change back.
They make mention of the prefab being a template, and this would kind of make sense, but I agree with you that if you can change some details in the Inspector, it would make sense to be able to rename it also, if that field is available. As per the staff member from Unity who replied in that link above, it may make sense to remove that functionality if it isn’t really intended.
So, yeah… name them better in the first place!