"What's in a name?" is an idiom. As Elise indicates above, it means that something is the way it is, regardless of the name. In other words, even if you call a rose, "Tuesday", it will still smell like a rose.
On the other hand, the passage you quoted above is ironic. It actually challenges the idiom. In fact, it is arguing against the notion that names do not matter. Former US president, Barak Obama, is arguing that indeed names do matter, and that "Redskiins" as a name is offensive to the public (and in particular to the native Americans). For this reason, he is effectively saying that the team ought to change its name.