Functionally all works fine but the issue I am having is that in the UI they are both shown with the same name and I don’t know how and where to change it
Yes, for future reference not all entities will have the gear icon. The gear icon is only available for entities that are created by components that generate a “unique_id” that gets stored in the .core.entity_registry file. There aren’t that many components that do that yet.
As you found out the rest of the entities can be (have to be) modified using the customize section of your configuration.yaml or you should be able to use the “customization” section in the “configuration” menu in dev-tools.