The name does not mean just 'gem', but it is Hebrew for a pearl.
― Anonymous User 5/15/2015
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Other forms are Penina and Pnina, both much more common than Peninnah. In Hebrew, it's pronounced p'NEE-na, with a very short space between the P and the N.
A famous bearer of the name Pnina (a more common variant form in Israel) is Pnina Tornai, a wedding dress designer. She specializes in over-the-top, glitzy, luxury gowns and is featured on the TLC show "Say Yes to the Dress."