No the Daylightmap names do not come from wikidata.
(The openmaptiles and e.g. also the openmaptiles-planetiler process once had wikidata preferred over osm as default but that is now configurable.)
I was rather looking into this process here that may have been the process they finally decided on for daylightmap localized names: Additional Translations in Daylight
And if you remember my question about city names in Arizona on the osm us slack language channel about Vietnamese: here is the current daylightmap answer for a Vietnamese (latin) example:
And you will find many more examples in their ~39000 localized names that will result in a “huh, wait, what is that?” moment … all those are currently baked in in daylightmap planet.osm.obf where the feedback process (->daylightmap->esri->esri language experts->esri->daylightmap) seems rather cumbersome and complicated and long-running esp. if you compare the process with just changing an osm tag 
(ok yes, I understand that QA is cumbersome).
So in general I think that the osm community is for these kind of problems actually a better QA than a small team at daylight that for sure cannot handle all those languages (but in many other areas do a great job in QA). For that, I’m not convinced that this is baked into the daylightmap planet.osm.pbf (and it will get way worse with overture).