This article needs to be split into two: one about the person, the other about the exclamation.
These omissions are so great that the article's factual accuracy has been compromised. Check out the discussion page and revision history for further clues about what needs to be updated in this article.
Geronimo was a Native American friend of the Doctor's, also known as Goyaale (The One Who Yawns). (PROSE: The Hopes and Fears of All the Years) The Doctor knew him as early as his eighth incarnation. The Doctor would occasionally talk about him as a lead in to shout "Geronimo!" (AUDIO: Storm Warning, PROSE: The Hopes and Fears of All the Years, COMIC: The Golden Ones)
It occurred to the Eighth Doctor that Geronimo would have been puzzled to know he would be remembered mainly by people who were about to fall from a great height. (PROSE: The Shadows of Avalon) The Eleventh Doctor used the expression following regeneration when his TARDIS was plummeting to Earth. (TV: The End of Time) He would frequently use the expression. (TV: The Eleventh Hour, The Beast Below, etc.)