Nicknaming is an attempt to assert dominance over the other, and so this is why the minions of the Hoover-Nixon-Bush party prefer this name for Democrats. It is done simply because it is irritating.
It is "dog whistle" politics. The ordinary person does not hear it, but for activists on both sides of the aisle, the petty dominance game is clearly audible. It invites an indignant response, which only serves to confirm their dominant position. "How can anyone be upset about such a minor matter?" And in that exchange, which they invite, they remind everyone of how "some people are just too sensitive" -- which is code for racial politics, and political correctness.
Let them clown. After all, he was giving up the gavel.
I don't think that they realize how wide and how broad the repudiation of the Hoover-Nixon-Bush Party is going to turn out to be. They think that if they go back to the tactics and rhetorical styles that they used as they rode into power, that they will reverse their current fortunes. I don't think that is going to happen.