This is an official answer by QuranicNames.com Staff
For Sheza please see: Is Sheza an Islamic name?
There is no Arabic name that sounds like Shasmeen.
Sha in Farsi means king, top, highest, and Sameen means valuable, precious, so Shasameen would mean "the most precious." I have never seen this phrase, however, but you are free to use it if you like it. Sameen comes from Arabic Thameen, which is an indirect Quranic word.
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