Good question, I haven't heard, but the entire gameday experience will be different. We got a taste of it last year before the name came back for the rest of the season. I was at the UW series, and remember how weird it was seeing the spinning ND logos on the ice instead of the logo, and how Looker didn't say SIOUX but the students added it to announcements.
Instead of a "Lets Go Sioux" chant, I can see a "U-N-D" chant becoming more popular. Strange times ahead. You wonder how long the masses will hang onto the old traditions before it feels weird. I compare it to someone dying, and you leave everything as it was before they died. Just not gonna be healthy, and after some time, you put away the deceased persons clothes and change the house around, etc. You can count on seeing SIOUX jerseys at hockey until the day you die, this I guarantee.
Edit: And NO, I am not saying losing a sports nickname is equivalent to someone dying, it was just an analogy about losing something and moving on.