>>29215410He's a Brazilian.
Olivia is used among Italians, Spanish and Portoguese in general, but ain't that rare among the Anglosphere.
I don't understand where is the type pun however unless subtle and less explicit.
The olive, known by the botanical name Olea europaea, meaning "european olive", is a species of small tree in the family Oleaceae, found in the Mediterranean Basin from Portugal to the Levant, the Arabian Peninsula, and southern Asia as far east as China, as well as the Canary Islands, Mauritius and Réunion. The species is cultivated in many places and considered naturalized in all the countries of the Mediterranean coast, as well as in Argentina, Saudi Arabia, Java, Norfolk Island, California and Bermuda.
She could be a Caribbean too.
Olea europaea contains a seed commonly referred to in American English as a pit or a ROCK, and in British English as a STONE.
So far olive oil can be still obtained by using the classic oil mill method, the oil mill is also made of STONE.