I may be wrong, but I believe the name of the type family is simply Times New; the name of the italic face would then be Times New Italic rather than the contradictory Times New Roman Italic. It’s strange that the name of the roman face specifically is always used; I’d suppose it’s merely because that’s how the digital fonts were inadvertently named? Times New Roman has been the name in dropdown menus, and most laypeople are unfamiliar with roman as a term of art, so there’s no reason people wouldn’t use that name. But I wonder how the digital fonts came to be named Times New Roman rather than Times New.