WaitForChild should return if an existing child has its name changed to what you're looking for

Feature Requests Engine Features
#1

I can’t imagine a use case where this behavior wouldn’t make sense. Especially considering that if you were to do WaitForChild after the name was changed it would return that child.

#2

Definitely!

On the same note, why does WaitForChild not work with an object in nil. Funnily enough this has only been an issue for me when relying on ROBLOX services such as an object going into StarterGui.