>(the Falcon 9 also is the second iteration of the Falcon rockets, not the ninth, so…)
Falcon 9 has nine first stage engines, Falcon 1 had a single engine. It's not a version number.
Edit: I had to look it up because Saturn 1 is not a single engine vehicle. It turns out that the Saturn V is design C-5 of the Saturn family of rockets, with A, B and C1-4 designs preceding it (not all designs where built), so the "V" in Saturn V is basically a version number, despite the Saturn V first stage having 5 engines
The "Falcon" name dates back to many years before the BFR concept. Then the BFR started out as "Big Fucking Rocket" and the F was retroactively changed to Falcon as a tongue in cheek way of keeping the acronym in respectable conversation. That said, BFR was always just a descriptive placeholder.
Back in the 2010s Blue Origin had a naming scheme after the pioneering flights of American astronauts:
The suborbital rocket New Shepard is named after Alan Shepard who was the first American astronaut and whose flight was a suborbital arc.
New Glenn is named after John Glenn whose first flight was the first orbital flight.
There was also talk of a New Armstrong rocket, although Neil Armstrong wasn’t the first American to "reach" the Moon. But then together with Buzz he was the first to land and the first to walk. I don’t know if New Armstrong's still getting developed.
