Hi @JMatazzoni (WMF), The easiest way to check how a certain name:xx is distributed is using taginfo. Here's all tags containing "name". name:en is the most common, with 2.6 million tags, and if you click it and click map tab, you will see it's fairly well distributed.
But the most other languages are far from it - name:ru, 2nd most common, seems to be only present in the eastern Europe - probably because editors there tend to add it together with name.
In general, several map companies have said they have to rely on Wikidata for internationalization. The process is fairly simple - just use Wikidata tag to lookup the name if its not present.
There is no way AFAIK to preview it, at least not on OSM site. OSM is using a fairly dated tech, and cannot easily show multiple languages.