Origin: Romanian, French, Jewish, Russian, Japanese
Meaning: possibly from Romanian soare meaning “sun”.
I’ve also seen it as a surname. It could be French in origin, from Old French sor, a diminutive of Sorel, meaning “chestnut”, originally a nickname for someone with reddish hair.
It also has a different etymology, a Jewish surname derived from a metronymic of Yiddish female personal given name Sore, from Hebrew name Sara meaning “princess”, with the Slavic suffic -in. From what I could find, it seems to be (or used to be) very popular in Russia, especially Belarus.
Sōrin (宗 麟)also seems to be a Japanese masculine given name, such as Ōtomo Sōrin (who also went by other names), who was a daimyo of the Ōtomo clan in the 16th century (1530-1587). I couldn’t find any meaning on his name, though sōrin is also the vertical shaft on top of a Japanese pagoda, usually made out of bronze or stone. It means “alternate rings” with the kanji used (相 輪).
Sorinel is a pet form of the name.
Sorina is the feminine form of the name.