I read they declined it because someone else had the trademark already (he was trying to guess the name), and because one of the College Military games where Military colleges go against each other is called the Commander.
BUT from something I read, the owner of the trademark claimed he would let the team have it at no cost (which is crazy as it cost him something to get it, at minimum, get reimbursed) but if true, that hurdle can be passed, and it's believed that a rebuttal argument might be able to get past the college game, as one college game per year is not likely to get directly confused with a Professional team. So it's potential to get around these hurdles.
My preferred method would be to rename them as Commanders isn't a great name (and currently it's an insult to real Commanders, at least as long as Snyder is running it) and the more we can erase Snyder from records books the better.
Fans wanted it to be Redwolves. But currently Arkansas State has that trademark, but the Washington team did not even ask if they could work out an arrangement to share it.... they just went that's taken... but really it's probably because Snyder knew what he wanted to name the team the entire time after reports he wanted to name it after the Military (check) and his favorite President (Commander and Chief... check).
But one of the NFL teams should be named after a canine... so many birds and cats, but no canines?