I was thinking maybe the author also intended to incorporate "Pan-Am", as in Pan America, into the name of the country as well, since Panem seems to include all of the former USA, and possibly Canada as well.
That reasoning does not make very much sense. As you say, Pan-Am would mean Pan-America, which translates to "The complete/whole America". From wiki:
The Americas, or America, also known as the New World, are the combined continental landmasses of North America and South America, in the Western Hemisphere.
Panem however only covers North America, so it seems like quite a stretch to name it Pan-America.
Even if you take into account that many US Americans like to limit the term "America" to the USA, the prefix "pan-" clearly indicates that you mean the whole thing, as in Pan-Africa or the Pan-American Highway.
Together with the fact that there seems to be no evidence for a third meaning in the books or the movie, one can conclude that most likely this was not an intended meaning of Panem.
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