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Yes, you certainly are able to derive the origin of your name from that of Chimene. The etymology of a name is its history. In your case, the history of Shamine is clearly that it was derived as a respelling of Chimene, so it would go back to the same original meaning as Chimene.

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Of course, the movie character is more relevant to your father's reasons for naming you what he did, so the meaning to him would be based on what that character was like. But you are quite free to trace back the origin of the name further if you are able.