i'm pretty sure the branding is just to filter anyone that isn't loyal to trump, anyone that doesn't agree with the new term is easily identified then slowly set aside.
This is also close to the authoritarian "make people say absurd things as a demonstration of power over them" playbook.
They do this (at least at first) to pull people out of their staff who would slow them down or fight them. Then they expand the scope, where they hope to reach the entire population.