As a political scientist, what interests me here is the contrast between public opinion (6 to 1 against a change in name) and the politics. One might characterize this as the difference between position and momentum. The Redskins name still hasn’t been changed, so in that sense the policy is congruent with public opinion, but there definitely is a sense that the supporters of the team name are on the retreat.
One might explain this via an elite-opinion or conspiracy theory story — the idea that supporters of the name change have power in the media and thus can drive the discourse in their direction — but I don’t buy it. It seems to me that there’s something about a change in opinion that has an effect, distinct from the average level.
Another example that comes to mind is the death penalty. It is still more popular than not, but it’s been my impression that, for several years, supporters of capital punishment have been on the defensive.
I don’t have any sweeping conclusions, but I think these sorts of examples are useful in helping us understand the connections between political science and policy (whether enacted by public or private institutions).