Customize field names in backend profile edit page through function.php [duplicate]

What you need to look at is hooking into the user_contactmethods filter.

Perhaps something along these lines:

function test_new_contact(){
  $user_contactmethods = array(
      'aim' => __('AIM'),
      'yim' => __('Yahoo IM'),
      'jabber' => __('Jabber / Google Talk'),
      'twitter' => __( 'Enter Twitter ID' ),
  );
  return $user_contactmethods;
}
add_filter( 'user_contactmethods', 'test_new_contact' );

Note the “core” user contact methods should be included in your filter function, unless of course you want to remove them … then simply do not include them at all.