init_arg is used to tell Moo what key will get passed to the constructor for that attribute.

use v5.16;

package Person {
   use Moo;
   has "nick-name" => (
      is       => "ro",
      init_arg => "nick",
      reader   => "nick_name",
   );
};

my $robert = Person->new(nick => "Bob");     # init_arg
say $robert->nick_name;                      # reader
say $robert->{"nick-name"};                  # attribute name (direct 
+hashref access)
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Setting init_arg to undef means that the attribute cannot be passed to the constructor at all. (And if the attribute is also read-only, so there's no writer method, you should probably be setting a default for the attribute too!)

(And this is not Moo-specific. Moose and Mouse have the exact same features.)