Costas called the "Redskins" name "an insult" and "a slur" and said the nickname does not honor anyone.
Here's a partial transcription (via Deadspin):
Objections to names like Braves, Chiefs, Warriors and the like, strike many of us as political correctness run amuck. These nicknames honor, rather than demean. They're pretty much the same as Vikings, Patriots, or even Cowboys. And names like Blackhawks, Seminoles and Chippewas, while potentially problematic, can still be okay provided the symbols are appropriately respectful. Which is where the Cleveland Indians, with the combination of their name and Chief Wahoo logo, have sometimes run into trouble.
A number of teams, mostly in the college ranks, have changed their names in response to objections. The Stanford Cardinal and the Dartmouth Big Green were each once the Indians. The St. John's Redmen are now the Red Storm. And the Miami of Ohio Redskins-that's right Redskins-are now the RedHawks.
Still, the NFL franchise that represents the nation's capital has maintained its name. But think for a moment about the term "Redskins," and how it truly differs from all the others. Ask yourself what the equivalent would be if directed towards African-Americans, Hispanics, Asians, or any other ethnic group. When considered that way, "Redskins" can't possibly honor a heritage or noble character trait, nor can it possibly be considered a neutral term. It's an insult, a slur, no matter how benign the present day intent.
And here's the full video: