It's just one of their many tradtions - they have never worn names on their uniforms and it is not required. The Giants don't have names on the back of their home uniforms so it's not just the Yankees.
Wow amazed no one got this exactly right yet. The Yankees dont wear there name on there backs because the Yankees are a team, its to promote team effort & not individuality.
Tradition. Same reason their only two uniforms are home white with pinstripes and road grays. No alternate jerseys, no alternate caps, nothing like that...