The surname has independent origins in different regions of Italy and is very widespread throughout the peninsula, with a particularly strong presence in the south. The consulted works concur in deriving it from the Latin word oliva, referring to the fruit or the tree of the olive (Olea europaea). The motivations behind its adoption are diverse: it could allude to someone who produced or sold olives, to a person with an olive complexion, or to someone who lived near or cultivated olive groves.

E. De Felice and F. Miranda further note that, for many surnames of this group, the immediate base is not the fruit or tree directly, but rather place names formed from oliva and ulivo, such as Oliva Gessi, Oliveto, or Olivetta San Michele. Both scholars also observe that, in western Sicily, the surname may derive from Sant'Oliva, a martyr of Palermo. Miranda adds that the name was probably introduced by the Normans — the form Olive was common in medieval France — and that it is linked to the cult of Saint Rosalia, frequently represented with an olive branch.

E. Rossoni indicates that the surname may also derive from the Renaissance given name Ulivus, Olivus, or Oliva, and documents the Counts Oliva at Pennabilli, in the area of Pesaro-Urbino, from the year 1500, as well as family lineages in the northern part of the area of Como from the year 1600. R. Brondolo proposes that the surname may alternatively stem from a matronymic use of Oliva as a given name, an origin documented in northern Italy.

It is recorded that the root olivarius refers both to the olive tree and to the person who cultivates it, and that some derivatives also stem from the medieval personal name Olivarius, documented in Pinerolo, near Turin, as early as 1040. The forms Olivus, Ulivus, and Oliva are also attested in the account of the Passion of Saint Arialdus. A. Bongioanni suggests that some surnames related to Olivier may carry French or even Germanic roots, and that the name Olivier gained currency in Italy through medieval French epics such as the Chanson de Roland, in which Olivier appears as the companion of the hero Roland.

The surname has given rise to numerous variants with distinct geographic distributions. Oliva is found throughout Italy, especially in the south and in Liguria; Olivi and Olivo are rooted in the Veneto and in Padua, with Olivo also present in Calabria and Sicily; Ulivi is typical of central and northern Tuscany, especially in Lucca, Florence, and Forlì; Olivari appears in the province east of Genoa and in Brescia; Oliveri concentrates in Sicily, Liguria, and the areas of Alessandria and Cuneo; Oliverio has a significant presence in Calabria; Olivero is widespread in Piedmont and central-western Liguria; Olivieri is extremely common throughout Italy; and Oliviero reaches its highest concentration in Campania, particularly in Naples.

Further variants show more localized distributions: Olivati and Olivato are found in Verona, Padua, and Venice; Olivetti has branches in Turin, between Brescia and Verona, in the area of Ancona, and possibly in Rome; Olivetto is typical of Vicenza and Padua; and Oliveto is characteristic of the areas of Potenza and Cosenza. The suffixes -ati and -ato, as in Olivati, Olivato, and Ulivati, function as patronymic or matronymic markers signifying "son of," referring to an ancestor named or nicknamed Oliva, Olivo, or Ulivo.