If Trump decides to set up a new party, let's say "American People's Party" (members will be called Americans, LOL)
There's no chance he would allow it to be named anything that didn't include "Trump".
I think your underestimating how divided the Democrats are though. It's not all that different from the Republicans right now. The moderate Dems and Republicans could end up being the third party, especially with Biden in charge.
The Trump party would be middle of the road. Trump is more of a 1990s Democrat than a Republican. His support is largely from the industrial workers that used to be Democrat until the Democratic Party abandoned them.
What are Trump's positions: Bring the industrial base back home; don't be involved in foreign intervention; and secure the borders.
His position does not attract the global capitalist aspect of either the Democratic or Republican Party.