After doing some reading, I see where my mistake was. I found documentation saying that the name tag "should not describe or label the feature" and should instead be the common name of the feature. So although it seemed counterproductive to me, it now makes sense that the blaze color should not be the trail name.

However, I still think there is somewhat of a grey area if the trail has an official name and if that should be used in the Name tag. The documentation also says that one source of a primary name is "The name of the feature on a sign elsewhere, such as a fingerpost".  In the case of the blue Salmon River trail, there is a posted sign by the covered bridge saying the official name of the trail. On the other CFPA trails, there are also official signs with the trail name. For example, on the Shenipsit trail, there are blue sign posts and/or wooden signs with the trail name posted at almost every road crossing. Why wouldnt this be official enough to include as the Name tag based on the definition of the Name tag? This grey area could also extend to places that have official trail maps, as the trail name on the official map is the common name. This seems to be analogous to road names, where the common name tag is what is posted on the street sign and visible on official maps.

There are already many cases of the trail name being the Name tag in OSM. For example, most of the trails in the White Mountains in NH have both Relation AND trail name. This information exactly matches what is on the wooden signs at the trailheads/junctions and also matches what is on the official paper maps. The Relation info provides the detailed trail info and the Name tag provides the official, signposted (or mapped) trail name. Just like a Relation could be used for a bus route to connect Named roads, a Relation is used for a hiking route to connect Named trails.

In addition to having the correct Relation information, I think it still makes sense to have the trail name as a Name tag (ONLY if its an official named trail with signage and/or an official map). What are your thoughts on this?