Apparently the Greekth font was created from the old open source MS Core fonts version of Times New Roman Bold.
When they did this they did not update all the name fields inside the font file.
So some of the fields still say Times New Roman which is causing the confusion.
This is what I found in one version ...
Unique Font Indentifier: Monotype:Times New Roman Bold:Version 1 (Microsoft)
PostScript Name: TimesNewRomanPS-BoldMT