Something like:

use warnings;
use strict;

package PhaseManager;

sub new {
    my ($class, @phases) = @_;
    my %phaseHash = map {lc($phases[$_]) => lc($phases[$_ + 1] || '')}
        0 .. $#phases;
    
    return bless \%phaseHash, $class;
}

sub Next {
    my ($self, $phase) = @_;
    
    die "Unknown phase '$phase'" if !exists $self->{lc $phase};
    return $self->{lc $phase};
}

package main;

my $manager = PhaseManager->new (qw'first second last');
my @testPhases = qw'first Second LAST FUBAR';

for my $currPhase (@testPhases) {
    my $nextPhase = $manager->Next($currPhase) || '<No next phase>';
    
    print "Phase '$currPhase' goes to '$nextPhase'\n";
}
[download]

Prints:

Phase 'first' goes to 'second'
Phase 'Second' goes to 'last'
Phase 'LAST' goes to '<No next phase>'
Unknown phase 'FUBAR' at D:\Delme~~\PerlScratch\delme.pl line 17.
[download]