Only 10% of Native Americans are offended, so... yay? The NFL is only offending a quarter of a million people?
I think roughly 10% of Americans believe Elvis is still alive. You can't get unanimity on
anything. But if you're down around Elvis-Lives levels, chances are it's not an urgent national (or, more to the point, legal) priority.
Tyranny-of-the-majority issues are impossible to form a bright line on. There was a point in time where an overwhelming majority of adults in the US would have endorsed exterminating native americans, or japanese-americans, or americans whose ethnicities trace to muslim-majority countries. Or at least deporting them. One of the best aspects of the US constitution, in my view, is how broadly the 14th amendment's equal-protection language has been interpreted in recent decades to protect the interests of small minorities, the accommodation of whom might be inconvenient and easily trodden upon.
The government awarding of a trademark is a pretty light touch, on the spectrum of government action. It seems to me that most people who want to force the Washington franchise to change their nickname want to use the tools of government to legislate public morality, effectively. That despite it being a private entity, they want to act as if it were a public one in terms of the remedies they have available, and are using this trademark thing to shoehorn in a government-level standard of review to private speech. As some of the articles covering it have pointed out, there are some trademarks that have been awarded that are far more offensive, at least to most people. So I'd probably expect that it would need to be a pretty obnoxious level of inconvenience to native americans - way above this 9% shown by polls - in order to justify crossing that public/private chasm here. So in that sense, the poll does have plenty of weight with me.
I think the activists seeking name change are missing the forest for the trees. The way bad private actors have been shamed into action in the past has been with protests, boycotts and public humiliation. They already have the media on their side! Burn Snyder in effigy outside the stadium on game days, make sure it makes the news. Stage a season-ticket-holder walkout a la Liverpool. The team sucks, so give people an additional righteous-sounding reason not to renew their tickets and let them declare that publicly, give them the shield of respectability in order to make a personal-entertainment decision. This focus on the trademark is really kind of a sideshow from where the real action ought to be, in my view.