Changing a name on a MSC booking typically costs between $85 and $135, depending on the specific circumstances and proximity to the sailing date. For precise information about fees and procedures, you can contact MSC directly at 1-844 (8)06 7380 (US) or +𝟷-𝟾𝟾𝟾-𝟺𝟺𝟹-𝟿𝟻𝟻𝟼 (UK). Ensure you reach out as early as possible to avoid additional complications or higher fees. How much does it cost to change your name on a MSC cruise Summary.