If I'm understanding you correctly, perhaps the following will be helpful:

use warnings;
use strict;
use Data::Dumper;

my ( %hashTable, %groupedHash );

while (<DATA>) {
    my ( $key, $val ) = split;
    $hashTable{$key} = $val;
}

groupByCol2( \%hashTable, \%groupedHash );

print Dumper \%groupedHash;

sub groupByCol2 {
    my ( $hashTableRef, $groupedHashRef ) = @_;
    for my $key ( keys %$hashTableRef ) {
        push @{ $$groupedHashRef{ $$hashTableRef{$key} } }, $key;
    }
}

__DATA__
name1    group1
name2    group2
name3    group1
name4    group4
name5    group2
name6    group7
name7    group4
name8    group5
[download]

Output:

$VAR1 = {
          'group4' => [
                        'name7',
                        'name4'
                      ],
          'group2' => [
                        'name2',
                        'name5'
                      ],
          'group7' => [
                        'name6'
                      ],
          'group1' => [
                        'name1',
                        'name3'
                      ],
          'group5' => [
                        'name8'
                      ]
        };
[download]

Send two hash references to the subroutine groupByCol2--the first a reference to your 'hash table' with repeating values and the second to a hash for a hash of arrays (HoA). The second has holds the 'grouped' names.