E. De Felice links this surname to the place name il Sodo, common in Tuscany as the name of small centres and localities. The term comes from Tuscan sodo, in turn from Latin solidum, meaning "untilled, hard and compact ground".

E. Rossoni proposes instead an origin from the medieval name Sodus, documented in an inventory of goods of the year 1301 in Chiusi. According to this reading, the name evoked the idea of animus ("spirit, courage") and was chosen by parents who wished a marked firmness of character for their child. Rossoni notes that Sodi is well represented in Tuscany, with a presence in Florence, Pontassieve and Scandicci in the Florence area, in Grosseto, in Arezzo and Monte San Savino in the Arezzo area, as well as in Pisa, Piombino in the Livorno area and in Siena. The variant Sodo, for its part, has specific areas in the Arezzo area, in Rome, in Naples, in the Basilicata region and in the Lecce area, in the localities of Gallipoli, Galatina and Nardò.