Neither Jepson or Munz offer a meaning for this name, but thanks to Umberto Quattrocchi and Jaeger’s Source-book of Biological Names and Terms, we have the following: Sesuvium, land of the Sesuvii, a Gallic tribe from west of the Seine. I have no idea how this name came to be applied to this genus however
Species
portulacastrum
Michael Charters infers that the meaning of this comes from the genus name Portulaca and the astrum, “star,” so would indicate a Portulaca-like plant that has star-shaped flowers