Geronimo
This article needs to be split into two: one about the person, the other about the exclamation.
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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.)