That little obit is wrong. He didn't start with the Drifters. Before that, he was lead singer of a group called The Five Crowns. He was Benjamin E. Nelson at the time.
In 1958, the Crowns were opening for the Drifters, who were already a big draw. The Drifters' manager, George Treadwell, had been battling with the group's members for months over several issues (including excessive drinking), and one night, during a show at the Apollo Theater, one of the Drifters cursed at the theater's owner. Treadwell, who owned the rights to the name Drifters, promptly fired the entire group, turned to the Crowns and basically told them, "Congratulations! You're the new Drifters!"
That's when Ben E. Nelson became Ben E. King. I always thought it was because his former group was the Crowns (Get it? King? Crowns?) but I just read something that said it was the surname of his favorite uncle.
He wasn't with the Drifters all that long -- less than two years, I think -- but he wrote and sang a number of their big hits of the time, including "There Goes My Baby" and "Save the Last Dance for Me," which was the Drifters' only No. 1 pop hit.
His first big hit as a solo act was "Spanish Harlem," followed, of course, by "Stand By Me."