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.
Re: "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."
The name of the typeface really is Times New Roman. The roman variant is called Times New Roman Regular and the italic, Times New Roman Italic (which I agree is awkward).
The reason for this is trademarks: "Times" was a registered trademark of Linotype and so when Monotype developed a similar typeface, they used and trademarked "Times New Roman."
Some time ago, I forget when, Monotype acquired Linotype and so is now the holder of both trademarks.
Don't know if Butterick's article mentions this or not. I've read it but not recently.
Replying to my own comment because I'm wrong. I thought that Times came first and Times New Roman later, but according to this article from the New York Public Library, the typeface was designed only once (by Stanley Morison).
The metal punches were then created jointly by Linotype and Monotype, which each sold these under different names (and registered trademarks), Times by Linotype and Times New Roman by Monotype.
IIRC, the Abobe Postscript font was simply called "Times", so that is usually what Macs had installed. Microsoft Windows shipped with the Truetype font called "Times New Roman", which was similar but not identical to the printer font.
