This could probably be refactored more elegantly, but it seems to do the job in a single pass without undue complexity.

use strict;
use warnings;

my @values = qw( 5 3 2 12 2 );
my @names  = qw( Cat Bat Cow Dog Rat );

my $min;
my @indices;

foreach my $ix ( 0 .. $#values ) {
  if( ! defined $min or $values[$ix] < $min ) {
    @indices = ($ix);
    $min = $values[$ix];
  }
  elsif( $min == $values[$ix] ) {
    push @indices, $ix;
  }
}

print "Lowest value: $min\n";
print "$_ => $names[$_]\n" for @indices;
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