If we adopt their language because things are already bad we are saying that their power is now the only reality that matters, we are giving up any form of resistance. We killed people under the name of Department of Defense too.

Giving them the name is giving them the legitimacy to continue to justify the violence, and signals to the rest of the population that no one is coming to help and the new order is absolute. Mind you, this is mostly the fault of complicit media going a long with the name change rather than individuals here on HN, but whether its a true description of reality or not isn't important, whats important is any form of resistance to stop giving legitimacy to the regime.