Just to make sure I fully understand:
When the people that put the name on the trail also are the ones that use the trail most often, then I’d say, they can name their trail at wish. I observe such trails here sometimes, unofficial even illegal MTB downhill trails. The downhillers are the single users and spend quite some efforts on those trails. Are yours of that kind?
If on the other hand, the trail has lots of other users, then I’d consider that wrong. No idea though how to tag such intricacies: mtb_name:en perhaps? (That might even apply to the other kind just as well.)