I'm probably naive, but I think the whole "named after a soft drink" argument is overdone. I seriously doubt that a meaningful number of potential fans have chosen not to support the team because it's a marketing vehicle, and I doubt rebranding would result in a noticeable increase in support. At least it's a decent team name and logo! It's not like it's the 'New York Coca-Colas' or the 'New York Snapples.' And the argument about the team name having no connection to the community also rings hollow for me. New York Giants? Skyscrapers, maybe. New York Rangers? Nicknamed 'Tex's Rangers' after their owner, George 'Tex' Rickard, then president of MSG.
I feel like your last example runs counter to your point, since it is a name that has a direct connection to the team's history and arose organically. Also just because the name could be worse, doesn't mean it's good or not having a negative effect either.
I know for a fact it is a factor that has contributed to my loss of enthusiasm, and I've experienced people dismissing the team on those grounds. I guess we just disagree on our perception of whether or not it is a big enough factor to warrant consideration. I think it is significant enough, a lot of people disagree. Fair enough.