The story in FRI a long time ago was that Blinder was originally assigned to the Tu-128, but then it appeared at Tushino in 1961 carrying AAMs.
Meanwhile, the Tu-22 at Tushino was a surprise.
So the face-saving maneuver was to rename Tu-128 as Fiddler, reassign the name to the Tu-22, and let people know that, yes, we've been carrying Blinder on the books for a while,
As for Beauty, the story was that an air attache at the show said "wow, that's a beauty" and a press reptile within earshot ran with it.