As I recall from having been alive at that time, if you knew about the Holocaust--that is, the killing of 6 million Jews--then you called it the Holocaust. If you lacked knowledge of the word "the Holocaust", then you were also fairly ignorant of what happened, so you would be unlikely to refer to it at all. People did, though, make reference to concentration camps. That's a phrase that now is synonymous with the Holocaust, but in the past meant much more generally detention camps for large numbers of people. So in other words, people who were so ignorant as to not know the word "Holocaust", would also not know of the genocide. This makes me think of other genocides and how we refer to them. There's no special, commonly used word for the Armenian genocide, the Rwandan Genocide, the Biafran Genocide, or the Native American genocide. Some people today refer to the Cambodian genocide as "The Killing Fields". I don't know if that is attributed to the movie of that name, or if it pre-existed the movie.

By the way, if you check out Google ngram viewer (which shows the frequency of a word's usage across time, based on all the books, newspapers, etc. that google has scanned in), you'll see that the word "Holocaust" increases in use gradually over the course of years from 1800, but the increase is not HUGE after 1945. It's just slightly more. Then there's an increase in 1977, but it's not huge either. In 1986, it goes back down in usage quite noticeably, but "genocide" increases very strongly at that point and just keeps rising.

It is worth noting that the term 'genocide' itself was only coined during the war, by a Pole named Raphael Lemkin, who I believe lost family/friends to the Holocaust (although I don't think he was himself a survivor, I could be wrong).

He used the term genocide to describe the Ottoman killings and relocations in Armenia, which he similarly accused the Nazis of in regard to the Jews.