To The Wolf
There is a theory that there was no obligation to put the parshiot in any specific order, and that Rashi and Rabeinu Tam both for intuitive reasons,wanted to establish a unified order so that everyone would be performing the mitzvah in the same way. They came to different conclusions which of the ways this should be. Hence the two prevalent ways had no specific names for themselves, as there is no need to establish a specific name for a practice that is non-specific.