In short, I think this may be all you need:

$self->xml()->$_() for values %{STUFF()};
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You didn't describe the relationship between the various values and functions; what packages are in use; or what the functions do internally. I've made some (fairly gross) guesses for the test code below; hopefully, you can adapt this for your specific requirements.

#!/usr/bin/env perl -l

use strict;
use warnings;

package With::Xml;

sub new { bless {} => 'With::Xml' }
sub xml { print "With::Xml::xml(): @_"; $_[0] }
sub first_name { print "With::Xml::first_name(): @_" }
sub last_name { print "With::Xml::last_name(): @_" }

package main;

use constant STUFF => {
    name1 => 'first_name',
    name2 => 'last_name',
};

my $self = With::Xml::->new();

$self->xml()->$_() for values %{STUFF()};
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Output:

With::Xml::xml(): With::Xml=HASH(0x7f9b998040b0)
With::Xml::first_name(): With::Xml=HASH(0x7f9b998040b0)
With::Xml::xml(): With::Xml=HASH(0x7f9b998040b0)
With::Xml::last_name(): With::Xml=HASH(0x7f9b998040b0)
[download]