Wikidata did not continue with importing vernacular names because the use of capitals in common names are different per taxon/country. I am afraid it is not enough in the end but I will check next week.
If wikidata gets an update, will the names in EOL get an update too?
Yes, although EOL tends to lag behind Wikidata. Right now we are only updating it every few months; we should be able to pick up the pace once our newer, smarter harvesting code is in place.