Add the following script in your project and create a file with the ".blah" extension:

[ScriptedImporter(1, "blah")]
public class BlahImporter : ScriptedImporter
{
public override void OnImportAsset(AssetImportContext ctx)
{
var go = new GameObject(ctx.assetPath);
ctx.AddObjectToAsset("Root", go);
ctx.SetMainObject(go);
}
}

Drag and drop the created GameObject in the scene.
Rename the asset.

Actual result: the gameObject in the scene is renamed.
Expected: names are not changed in the scene.