c. 1200, "olive tree," from Old French olive "olive, olive tree" (13c.) or directly from Latin oliva "olive, olive tree," from Greek elaia "olive tree, olive," probably from the same Aegean language (perhaps Cretan) as Armenian ewi "oil."
Applied to the fruit or berry of the tree in English from late 14c. As the color of the unripe olive from 17c. Olive branch as a token of peace is from early 13c., an allusion to the olive leaf brought by the dove sent out by Noah from the ark. Olive oil "oil expressed from the pulp of the common olive" is by 1540s (Oliue oyle). In early writings oil of olive(s) was more common.
<a href="https://www.etymonline.com/word/Olivia">Etymology of Olivia by etymonline</a>
Harper, D. (n.d.). Etymology of Olivia. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/Olivia