Only Ichiro is allowed to use just his first name on the back of his uniform.
The Yankees and the Red Sox are the only teams that do not have players’ names displayed on the backs of their home uniforms. The Yanks also don’t have them on road uniforms. (As a corollary, the sales of scorecards in Fenway Park are especially brisk.)
Every team in MLB, however, is required to have numbers on players’ jerseys. This practice dates back to the mid-1920s, and was begun by the Yankees. At the time, the placement of a hitter in the batting order determined his number. So the leadoff batter was 1, the second-place batter was 2, and so on.
That’s why Ruth wore 3 and 4 was Gehrig’s.