Maybe, Im missing something, but why cant these trails have the name in the relation AND in the trail name? The Hop River State Park trail to the north has a Name Tag and Relation, so why cant these trails have it too? This is the official map from DEEP: https://portal.ct.gov/-/media/DEEP/stateparks/maps/DayPond2015rpdf.pdf 

In the OSM documentation it also says:
"Here are the usual sources of primary names:
The most prominent name on a sign posted on the feature itself, especially for a feature in the built environment.
The name of the feature on a sign elsewhere, such as a fingerpost.
Common or official usage, especially for a feature in the natural environment."

The official trail name seems to satisfy the requirements to add it to the actual Name in OSM.

For the Salmon River trail, just try using any of the popular outdoor apps/websites like GaiaGPS or Strava to create a course following only the Blue trail here. I bet that you cant unless you have already been here before and know the trails. Thats because those platforms only show the name tag and not the relation info. For example, on Gaia, you can even select the individual trail, but the only information that it shows is "Unnamed Trail". Therefore in areas with a lot of trails, it is super difficult to determine which trail is blazed or official until you actually go there. So while I would still agree we could include the Relation information, it seems WAY more important to also show the official name (which often includes the color) as a Name tag in OSM. I explored a lot of these trails and it would have been much easier for me to initially plan routes on the different platforms if I knew which trails were blazed and which trails were the official trails that matched the state park maps. By naming these trails, I was hoping to help other people that have never been on these trails before, so they could plan their routes and navigate effectively and safely.

Sorry for the long rant, I guess I am just frustrated that I spent hours over the past week naming all of the trails I have explored and then you just reverted all of them today. I think we should be able to label both the Relation and the Name. It seems that more data in this case would help more users (using different platforms that may not have relation info). Let me know if you think we could do both. Id like to contribute with my local knowledge and help end users, but I dont want to waste my time if you are just going to revert all my work.