Many years ago someone here proposed the best possible explanation: Ilia can read English. V'Ger never calls itself "V'Ger" until the probe arrives, after all. It might've just learned what that label meant and said when it absorbed Ilia (or was scanning the Enterprise library computer).
Though, apparently, some parts of the plaque were less obscure to it. It (or the Machine Planet) had been able to deduce its mission (not too difficult, it's a bunch of scientific instruments and a big transmitter with minimal ability to maneuver, not many things it could be intended for), and its point of origin (that damn pulsar map again).
Talking about the nameplate in the film, and the real Golden Record, I got a book and CD set of what was on it years ago, and I finally figured out what those three ovals were next to the word "Voyager 6" were. And now,
seeing the whole plaque clearly on a high-res widescreen version, I think I see what's going on. The setpiece in the movie doesn't have a Golden Record on it, which makes sense, because
it's ninety minutes of audio and
almost fifty images saying, "Humans built this! Humans that look like this, and live in a place like this! Humans made of meat! Carbon meat!" which would be a bit of a plot-hole. But if Voyager 6 was teleported across space (and possibly time), how would the Machine Planet figure out where it came from?
The left side of the name plaque has, mostly unobscured, the pulsar map to Earth from
the cover of the Golden Record (plus the diagram of a hydrogen atom illustrating the time-units used in the map to show the frequency of the pulsars, so you can actually interpret it). On the right of the name plaque are three ovals, which is one of the images encoded on the actual record,
maps of Earth's landmasses millions of years ago, in the present day, and millions of years from now. So they removed the record so V'Ger could still be confounded by the concept of life as we know it, but added the name plaque with the two pieces of information it would need from the record to know where it was going, and how it would know it found the right place when it got there.
God, I love how storytelling is like an iceberg, especially in a big movie with so many people on it like this all considering their little piece of it. There's so much thought that goes into everything, and you're lucky if even a tenth of it gets made public in interviews and making-of books.