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This is not from the surname or directly from Italy, but it is related to the Italian city, because it's from the cosmetics brand name, which was chosen by its American founders because of the city's reputation as a leading fashion headquarters:

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https://blog.mapleholistics.com/blog/milani-cosmetics-review/

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Once this became the name of a well-known cosmetics brand, its similarity in sound to newly-popular Hawaiian-influenced names like Kehlani and Leilani led parents to think of it as a great "different but not too different" sounding name for a baby girl. Other names derived from cosmetic brand names such as Chanel, Toccara, and L'oreal have become feminine first names previously for similar reasons.