There are two dimensions to this:
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Germany didn't exactly keep quiet about the Concentration Camps
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There were no reliable records about the Jews in Eastern Europe
I'll expand on that:
- Historians often divide the 12 years of the Third Reich into four parts regarding the establishment of concentration camps - what started as prison-like camps for political enemies turned to camps for people not deemed part of the Volksgemeinschaft ("Antisocials", homosexuals, Jehova's witnesses), then after the beginning of the war camps for foreign people, then for the Jews (this is an oversimplification, but it helps).
During the first of those periods, knowledge of these concentration camps wasn't hard to get. Infamous camps like Dachau even had Open House days for the population living nearby. The KZ Theresienstadt (in what is now the Czech Republic) was openly praised as a beautiful city, a "Jewish Ghetto for the Elderly" where, from 1942 onwards, all Jews over the age of 65 should live - all the while a quarter of the inmates died in Theresienstadt and nearly 90,000 were deported to death camps. A propaganda movie was filmed by a famous german-jewish director, Kurt Gerron, showing Theresienstadt as a wonderful place to live - most actors and the director were deported to Auschwitz shortly after the production was done.
So, to sum up, knowledge of organised extermination was rare, but knowledge of concentration camps was publicly available.
- Up until today, we do not know all names of jewish Holocaust victims, and we will never do so. We don't even know exactly where they came from, records aren't always kept strictly and a lot of them were lost - in more rural areas, people may have even never registered. A wide-spread argument by Holocaust deniers are some numbers from journals and almanachs about the number of Jews in the world which, according to those sources, has barely changed (or even increased) between the 1930s and the late 1940s. In fact, all those numbers are more or less educated guesses. And if we today, in one of the most prominent fields of historical research, can't figure out numbers more exact, than how should people during World War II have?
Brief summary: Americans knew about concentration camps (not death camps!), and they didn't know about the number of Jews in german-controlled territories.