^ I believe the only mention of a "bird of prey" in "Balance of Terror" was this:
KIRK: "After a whole century, what will a Romulan ship look like, Mister Stiles? I doubt they'll radio and identify themselves."
STILES: "You'll know, sir. They're painted like a giant bird-of-prey."
That's a long way from declaring "Bird of Prey" as the ship's official class designation.
And, if memory serves, no mention of "bird of prey" at all in "The Deadly Years" or "The Enterprise Incident." Were the Romulan ships featured in any other episodes?