How do I change the name on my @me.com email.com?
Assuming that you're trying to change your full name (and not the email address itself), you can follow the directions in this Cnet article:


  First log into iCloud.com, then click the Mail icon to open the
  Webmail application. In the Webmail application, click the gear at the
  top right and choose "Preferences" from the menu that appears, and you
  should see a window that appears with settings specific to your e-mail
  account. Click the Accounts section and you should see editable fields
  for Description and Full Name. Fill in your desired full name to
  display, and save the settings.
  
  
  
  Note: Image courtesy of Cnet


Your updated full name should then be used by the @me.com email address. The article also discusses how to change the displayed full name in the OS X mail client, but this example is a bit more generic.