The name Bourne came from Ansel Bourne, a preacher in Rhode Island, the first documented case of "dissociative fugue", a condition not unlike dissociative amnesia or dissociative identity disorder (multiple personality disorder). One day in 1887 he forgot who he was, started a new life in Pennsylvania under the name Brown, and opened a convenience store. About three months later, he woke up and not only remembered his life as Bourne, but forgot all of his life as Brown, and was quite confused as to why he was in Pennsylvania.
Matt Damon trained in the Filipino martial art Kali for the movie. Kali involves using the aggressor's energy against him and conserving your own energy.
Matt Damon climbed down the last 30 feet of the building himself, without a stunt double. He called it "the most gruelling thing I had to do."
Most of the US Marines in the Zurich consulate were actual Marine Security Guards assigned to embassies in Europe, at the request of producer Frank Marshall. They used their own uniforms, worked with the director on dialogue (eventually cut), and developed the tactics they use in clearing the embassy.
Doug Liman wanted the camera operator to be late moving the camera, adding an "edge" to the photography. So he didn't let him watch rehearsal - that way, he wouldn't know which character spoke next.