If a name tag is broken in OpenStreetMap, I can fix it in OpenStreetMap. If a name label is broken in Wikidata, I now have to fix it there as well, and get into edit wars with folk from Wikipedia who use different rules for naming things. So not only are there now two places to fix bugs, there are also two sets of sometimes conflicting policies for naming things. This is because for Wikipedia (which is Wikidata's sister project and has a large influence on it) it may make sense to call the Belgian district of Luxembourg 'District Luxemburg' in English (which is what OSMApp does via Wikidata), but on a map this region should just be labelled 'Luxemburg' (if using English), or preferably just 'Luxembourg' (the endonym). That it is a Belgian district, and not the neighbouring country can be made sufficiently clear by styling and geography.
After all, you don't expect the literal label 'New York City' for the city and 'New York State' for the US state on a map; just 'New York' for both, with styling and size indicating which is which. Any map which does want to render these names with their classification can do so by adding '(city)' or '(state)' to the label if they want to. It just shouldn't be part of the name in the data source.
Map labels are complicated, so leave that complexity to a project which deals with map data; i.e., OpenStreetMap.
This is a discussion more about data vs. maps, there are data purists in OSM as well. So the correct way to do it according to a large portion of OSMers would be to write out the full name.
After all, you don't expect the literal label 'New York City' for the city and 'New York State' for the US state on a map; just 'New York' for both, with styling and size indicating which is which. Any map which does want to render these names with their classification can do so by adding '(city)' or '(state)' to the label if they want to. It just shouldn't be part of the name in the data source.
Map labels are complicated, so leave that complexity to a project which deals with map data; i.e., OpenStreetMap.