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Both origins are correct. "Isabel" is a Latin form of Elizabeth, and can be found in various forms in languages such as Spanish, Italian, French, and Catalan. However, it also exists in a form completely unrelated to Elizabeth (Elisheva in Hebrew), as a dialectal variant of Jezebel. Just claim the first origin, and not the second one, if you want to use Isabel.

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The Wikipedia pages for both Isabel and Jezebel explain this.

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Hope that helped!