Rodríguez (usually Rodriguez in US Census spelling) is Spanish and Portuguese for “son of Rodrigo.” The -ez/-es ending is the Iberian patronymic badge, the same machinery behind Hernández or Martínez. Rodrigo itself is an old Germanic-rooted personal name that was thoroughly at home in medieval Spain and Portugal.
So the surname does not describe a job or a landscape feature; it freezes a father’s given name into a family label. Many unrelated Rodrigos produced many unrelated Rodríguez lines. Some Sephardic families later kept or readopted Iberian surnames after conversion periods, but the linguistic meaning remains “Rodrigo’s son.” That is the family-sendable core.