My recollection is that IR was not mentioned at all for the first few days and then for about a week, he was referred to only as a family friend. I don't think his identity was released for a couple of weeks. I will look for links...
ETA: July 27th:
http://www.ksl.com/?nid=148&sid=35680592
"Lemhi County Sheriff Lynn Bowerman confirmed Isaac Reinwand, 35, of Idaho Falls, was at the Timber Creek Campground on July 10 alongside Deorr's parents Jessica Mitchell and Deorr Kunz Sr. and his as yet unnamed great-grandfather.
The sheriff's office had previously withheld Reinwand's name, referring to him only as a family friend at the campsite."
July 13th: "friend of the family"
http://legacy.ktvb.com/story/news/local/idaho/2015/07/12/search-for-missing-2-year-old-continues-in-lemhi-county/30058523/
As near as I can tell it was July 26th or 27th that IR's name was released.