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The reason Levi works is because Jewish priests are decedents of Levites, one of the original twelve tribes of Israel. Levi, of course, being the patriarch of the Levites.

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Levites were given this special status because they did not bow to worship the golden calf when Moses ascended Mount Sinai. So... yeah, the actual name has different meaning but the historical meaning of the name Levi outweighs the etymology for your purposes.