First recorded (as “His Latest Flame”) by Del Shannon (1961).
Hit version by Elvis Presley (US #4/UK #1 1961).
From the wiki: “‘(Marie’s the Name) His Latest Flame’ was written by the songwriting team of Doc Pomus and Mort Shuman (‘Save the Last Dance for Me’, ‘This Magic Moment‘, ‘Little Sister’, ‘Teenager in Love‘) and was originally recorded by Del Shannon for the album Runaway With Del Shannon, released in June 1961. The more famous and more successful recording by Elvis Presley was released in August 1961.”
Elvis Presley, “(Marie’s the Name) His Latest Flame” (1961):