They write it that way to conform to their style guidelines, the NYTimes Manual of Style and Usage. Most style guidelines (Chicago, AMA, AP, etc.) have similar styles.
Oh, I'm aware, it's just strange to see his name as anything other than "Tim Cook." One would think exceptions should be made to style guidelines to ensure the reader doesn't pause and think, "that's just weird." Strict adherence to style guidelines doesn't always produce the best results.