Shinuchi (真打) is the auction-house and Kamunabi name for Magatsumi. The glossary already used the word. Reddit and YouTube still treat it as a possibly separate sword. It is not. Shinuchi means masterpiece, the headliner, the listing at the 208th Rakuzaichi. Kyora sells a title. Yura spends a title. The steel is Magatsumi.
Why the double name stays
VIZ keeps both. English readers meet Shinuchi first as an auction rumor, Magatsumi later as a person. The leak, the seal, the basement, the possession path: all of that is one blade with a billing. See Magatsumi, names in English, Rakuzaichi.