Quick: What's your neighbor's name? You know it, right? Yeah, we thought so—it's just kind of how things go with neighbors. You live next to someone long enough, and you're bound to know their name.
Well, unless you're Bruno and Gretel.
In The Boy With the Striped Pajamas, Bruno and Gretel are uprooted from their home in Berlin and move (along with their parents and hired help) to a house in Poland right next to Auschwitz, one of the largest concentration camps of the Holocaust. As far as neighbors go, this would be a tough one to miss—after all, it's filled with starving people, all wearing the same drab clothing and Star of David armbands, who are constantly corralled and yelled at by soldiers.
Because of this, the fact that neither Bruno nor Gretel can say Auschwitz, instead calling it Out-With, says a lot. These two clearly don't understand where they are—Bruno even thinks he's still in Germany until Shmuel clues him in. Plus, Bruno and Gretel think Out-With is the name of their house—not the concentration camp that lies on the other side of the fence. They may literally be neighbors with the horrors of the Holocaust, but the bubble of privilege they live in as the children of Nazis remains pretty impenetrable.
When Bruno asks Gretel what the name Out-With means, she says:
"Out with the people who lived here before us, I expect." (3.124)
On one hand, this is just further evidence of how oblivious these two are about what's going on around them. But on the other hand, it's a pretty poignant statement about what's going on around them, even if Gretel doesn't intend it as such: In the Auschwitz concentration camp, the Nazis are killing the Jews, trying to get them 'out' of the world. So while the name of Bruno and Gretel's new home is technically Auschwitz, Out-With speaks pretty aptly to what is being done there.