Was there ever a Valiant Barracuda?

Barracuda was a model of Valiant in 64 but not 65, even though the 65 had the Valiant symbols on the lower rear window trim and steering wheel, it was not a model of Valiant after 64.

As far as how they were titled, that depends on the state they were registered in and the person filling out the paperwork. I've had over a dozen of them over the years and not all were titled the same. I had some titled as just Plymouth 2dr, and some titled as Plymouth Barracuda, I've also had a Valiant titled as just Plymouth and a Duster that was titled as a Valiant.