Is it "Aogiri Tree" or "Aogiri Wood"? I've seen it translate to both in different sources when reading the manga. I think in the Anime it was "Aogiri Tree" but I can't quite remember.
The name is Aogiri Tree, also referenced to several times as just Aogiri. The name of the organization is Aogiri Tree because the manga and anime translated it into English as Aogiri Tree.