On the other hand, there are significantly fewer, but still many who claim descent from Rav Shmuel Ben Natronai, son in law of the RAVaN (R Eliezer ben Natan).
The name Natronai is of unquestionable Babylonian origin, and associated with the family of the Resh Galuta, who had patrilineal descent from David Hamelech.
The Otzar Hagedolim brings the tradition of a deposed Resh Galuta named Natronai exiled and appearing in Southwestern France in the Lunel/Narbonne area several generations – about 200 years earlier, and Binyomin of Tudela wrote of visiting Narbonne where (I’m quoting) the “Zerah Hakedosha” resides at about the time of R’ Shmuel’s father. So it isn’t definitive, but likely, that this name Natronai (extremely rare in Europe) belonged to a father to son descendant of David Hamelech.