The Rapaports have a shtar going back to the shach who had, as a matter of common knowledge, a shtar all the way back to Ezra. There are several Yemeni families who still have shtaros back to Ezra’s time. This means they are descended from kohanim whose yuchsin were checked by Ezra himself.
Sarfati means “the frenchman.” When a Jew from france came to Tunisia, he would have been likely to be given that name. The Rambam was known as Moshe ibn Maimoun (ben Maimon to us) HaSefardi. The Ari got the name Ashkenazi from his father who moved to sefardic lands from Europe.