Well, there were FZR models, so I googled for what that meant. Here is one possibility: Forza Rapid (Romanian car race)
However, I suspect they are just initials that meant something to Yamaha, maybe initials of the original designer??
Honda has CBRs, CBs. The CBRs are race replicas, so maybe Yamaha is doing the same here since this is a naked bike, so just FZ.
Somehow, I suspect we will never know for sure.
I think the Japanese to US naming convention goes back a ways. Again, this is my car knowledge, but may relate. And don't quote me on this, it's my own translation. Back when the Japanese automakers were making a push into the American market most of them choose a very feminine line of names for there vehicles. Consider some of Nissan's like the Fairlady (later know as the 350z), the Silvia (later know as the 240zx), the Skyline (later know as the GTR). This was post muscle car era where we were used to driving big Detroit names like Nova, Mustang, and Chevelle! And so it was hard for us to swallow our pride when we went to the track and said "My Fairlady is gonna kick your Mustangs a$$!" Doesn't sound very tough right? Or more like it sounds pretty stupid in this day and age, but consider the era and mind set back then. However, after performing surveys, reveiws, etc. the automakers discovered the issue and transition to model prefix naming convention. It doesn't mean anything special. It is simply the model number they had on the corner of their blue prints at the time. Another perfect example, the Mazda Miata. Some of you may have remembered it's first release in the early 90's with it's very... sky blue. No self respecting man was ever secure enough to go near that car, let alone drive one. A few years later they renamed it as the MX-5 and it is now the most raced car on American tracks today. (though everyone still knows its a miata, haha. But I'll have to admitt they are fun as hell to drive.)
So with all that being said, I would say Yamaha is doing the same.Perhaps the FY-07 never made to market, and instead we got the FZ.
I would say its just the internal production name...Mercedes calls their models W 123 for example but would never sell or market them as such....
So the first bike they build was the YA1 and then it just kept going YA 2 etc....YAT1 was a twin cylinder, once the fourstrokes came out they had the
production name XS etc etc