A number of bugs in there. First, you need to fix the code for initialising hit points in your constructor:

        _hp   => $arg{hp} || rand (10) + 2
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These are objects. You get your blessed object as the first parameter when a sub is called against an object so:

sub damage {
    my ($self, $hits) = @_;
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and you can use the object ref to acces the object data:

    $self->{_hp} - $hits;
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Taken all together your code ends up like:

use strict;
use warnings;

package Peasant;
use strict;


sub new {

    my ($class, %arg) = @_;
    my $objref = {
        _name => $arg{name} || "unknown",
        _hp   => $arg{hp} || rand (10) + 2
    };
    bless $objref, $class;
    return $objref;
}

sub damage {
    my ($self, $hits) = @_;
    
    print "$hits damage\n";
    $self->{_hp} - $hits;
   
}


sub name {return shift->{_name}; }


sub attack {
    my $self = shift;
    my $int = int(rand(5));
    
    print "$self->{_name} attacks for $int.....\n";
    return $int;
}

1;

package main;

my $henry = Peasant->new(name => "Henry", hp => "15");
my $joe = Peasant->new(name => "Joe", hp => "15");


$joe->damage($henry->attack ());
$henry->damage($joe->attack ());
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which prints:

Henry attacks for 1.....
1 damage
Joe attacks for 1.....
1 damage
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