I actually found out that the operator has a wikipedia page, so the easiest for data consumers is just to reference it, then no need to worry about languages, typos and different variation of names:
operator:wikidata=Q5260416
Just wondering—since the trails are only accessible after paying an entrance fee, shouldn’t this be reflected in the access tags? For example, highway=footway/path + foot=customers/permit + bicycle=no + horse=no.