Apple's insistence of hiding fonts installed by the OS is making it harder and harder for folks to use the fonts they not just want, but at times need to use.
Per VikingOSX's note, Times is still in the main /System/Library/Fonts folder as a TrueType collection, Times.ttc . A collection stores more than one typeface in a single desktop item. It includes:
Times Roman
Times Bold
Times Italic
Times Bold Italic
Then there's the /System/Library/Fonts/Supplemental folder, which holds the Times New Roman fonts. Which has the same four variations - Roman, Bold, Italic and Bold Italic.
They are distinctly different fonts with their own matching internal names. You should be able to see and use both, but Apple hides Times from the user.
In Office 365, this set of Times fonts are embedded in each app:
times.ttf
timesi.ttf
timesbd.ttf
timesbi.ttf
With fonts, the names you see on the desktop actually mean nothing. It's the internal names you see in your apps. In this case, the embedded MS fonts are actually another set of Times New Roman.
If you, for some reason, you need the slight visual difference of Times vs. Times New Roman, you're going to have to use a third party font the OS can't block you from seeing in your apps. Such as Adobe's Times LT Std set.
But really, with the way Apple is making it more and more difficult to use the OS included fonts, I would strongly suggest to never - and I do mean never - use any fonts installed by the OS. Always use third party fonts you have control of.