E. De Felice and V. Blunda agree that the surname derives from a Germanic compound with the elements hrod/hroth ("glory, fame") and rik/ricja ("power, dominion").

De Felice specifies that the surname was formed from the name of Germanic origin Rodrigo, attested in Italy from the 9th century as Rodericus and Rodoricus, of Gothic tradition, but consolidated in the type Rodrigo only in the late Renaissance through the presence and political-cultural influence of Spain. He notes that the Germanic name Hrotoriks, documented in medieval Latin as Rodericus, corresponds to the last Visigothic king of Spain (beginning of the 8th century).

De Felice adds that the type Rodriguez or Rodrigues, frequent also among Sephardic Jewish families, directly reflects the Spanish surname Rodríguez, derived from Rodrigo with the patronymic suffix -ez.

Blunda, for the Sicilian variant, derives it from the Germanic compound Hroth Ricja, with the meaning of "powerful through glory" or "famous lord." Blunda recalls Don Rodrigo Díaz de Vivar, the Cid Campeador (c. 1043–1099), a Castilian noble, the most celebrated Hispanic warrior of the Reconquista. He conquered Valencia from the Almoravids in 1094 and held it under his government until his death, an episode immortalized in the Cantar de Mio Cid, the first complete literary monument of the Spanish language, written around 1200. He also notes that the variant Rodolico presents the preservation of the intermediate consonant.