Global symbol "$input" requires explicit package name at /tmp/soap.pl 
+line 28.
Global symbol "$response" requires explicit package name at /tmp/soap.
+pl line 52.
Missing right curly or square bracket at /tmp/soap.pl line 53, at end 
+of line
syntax error at /tmp/soap.pl line 53, at EOF
/tmp/soap.pl had compilation errors.
[download]

You have a few problems with the server side of the code. The first big one, that won't show up even from 'use strict' -- you're printing. That's bad when you're doing SOAP, unless you make sure that they're valid headers. (and even then, I don't recommend it).

Anyway, to answer your initial question -- as SOAP::Lite does RPC/encoded, you need to hand off to a specific function that acts as a switchboard, that can look at the value of the field in question, and then passes off to your other functions. You're also using SOAP::Transport::HTTP::CGI when you seem to be using mod_perl, based on the '<s-gensym15/>' that was returned, and the URL that you used in the client.

Try something more like the following for the server:

#!/usr/local/bin/perl --

use strict;
use warnings;
use SOAP::Transport::HTTP;

SOAP::Transport::HTTP::Apache
  -> dispatch_to('Delivery')
  -> handle;

package Delivery;

use Data::Dumper;

sub byName {
  my ($self, @data) = @_;
  warn 'Delivery::byName : ',Dumper( @data );
  
  if ($data[0]->{'Action'} eq 'New Ticket') {
      return sendAcknowledgement();
  } else {
      return { error => 'Unknown Action' };
  }
}

sub sendAcknowledgement {
  return SOAP::Data->name(
      Acknowledgement => {
        createStatus => "OK",
        Received => "0",
    }
  );
}
[download]

It uses 'warn', not 'print', so the debugging info is sent to the webserver's error logs. Note that I've also used 'eq' not '==' for the string comparison. What you got returned was an empty hash, because $response wasn't defined. (which is why use strict is your friend) Also, in the client code, you're using a custom serializer, but you've never defined $serializer.