Trofimena

This given name is best known for being the name of the 7th-century saint Trofimena, who was born and raised on the island of Sicily. During her lifetime, Sicily was a province of the Byzantine Empire, where Greek was the primary language. As such, the original form of her name must have been Trophimena (alternatively Trophimene), especially if you take into account the fact that the Italian language did not yet exist in the 7th century. It only began to develop in the 12th century, which means that we should conclude that Trofimena is a later form and therefore the Italian form of Trophimena.

With that said, the name is clearly of Greek origin. It is most likely a compound name that consists of the Greek noun τροφή (trophe) meaning "nourishment, food" combined with either the Greek noun μένος (menos) meaning "mind, strength, force" (see Philomena) or the Greek verb μένω (meno) meaning "to stay, to remain" as well as "to last, to withstand" (see Menelaus). As such, the meaning of the name is either "nourishment of the mind" or "to stay nourished".

Alternatively, the name is a variant of Trophimina, a Latin diminutive of Trophima. This seems a bit less likely however, given the strong presence of the Greek language on Sicily both at the time and when it was still part of the Roman Empire (from the 3rd century BC to the 5th century AD). Sicilians were culturally and linguistically Greek and remained so during Roman rule and subsequently Germanic rule and Byzantine rule, which probably means that they (or at least those who did not belong to the Sicilian elite) had little contact with the Romans and their native language (Latin). As a result, they had little need to latinize their native Greek names or to re-hellenize Greek names that were latinized (as essentially would have been the case if Trophimena came from Trophimina).