I create a new symbol. I can rename the instances in the layers panel.
Then, I rename the symbol in the assets panel. This overrides the custom names of the instances of my symbol.

This behavior is inconsistent with the notion of instance in Adobe XD. When I change an element of an instance, all my instances are updated accordingly. There is no notion of a master symbol.

Why can I rename an instance one by one if all the names can be overridden when renaming via the assets panel wherease any UI change in an instance directly affects all the other instances. In one case, it seems there is the notion of master symbol whereas in the other, it's more a reference of all the instances.

If it's a real instance of a symbol, renaming all the instances should not be automatic. I have the same issue with a symbol drag-and-drop. It replaces all the instances with the new symbol whereas I juste wanted to replace one instance.

If there is no notion of master symbol, you should revise the renaming behavior which is not logical with the rest.