I've had this discussion with some Kenyan runner friends on MANY occasions. The Kalenjin naming practices (the Kalenjin tribe makes up the majority of top runners) work roughly like this.
1st name -- Anglo/Biblical name. Not used by Kenyans when dealing with other Kenyans.
2nd name -- Deals w/the circumstances of their birth, with a prefix attached. Men tend to have the prefix "Kip" while women have the prefix "Chep" or "Jep". Example: Kiptoo is a boys name that means born when visitors are around, while Jeptoo is a female equivalent to that. While in Kenya or around other Kenyans, this is their "First name" or the name that they typically go by.
3rd name -- Most often comes from the father. For boys, you simply take the prefix away from the father's second name. So, If your dad's 2nd name is Kiplagat, your 3rd name will be Lagat. For girls, they often just take the father's third name without any change.
Summary: David Kipkosgei Lagat would go by David when dealing with Americans, but Kipkosgei around people of his own tribe.
Granted things can vary, but this is the best of my understanding after many many many runs discussing this. Or, my buddies could just be screwing with me and this could all be off.