Adoot Koothrappali is the one of the three brothers of Raj and Priya Koothrappali and the other son of V. M. Koothrappali and Mrs. Koothrappali. He has never appeared on the show. It's unclear if Adoot is one of Raj's older brothers or his younger one. He was apparently very mean to Raj as a kid as he once left the door open and caused Raj's pet mongoose to run away.
His name was finally revealed in "The Sibling Realignment".