my %types;

while (<DATA>) {
    chop;
    m/(.*)\s([^\s]+)$/
        or next;

    push @{$types{$2}}, $1;
}

foreach my $type (keys %types) {
    print "$type\n";
    print "$_\n" for @{$types{$type}};
}

__DATA__
name1 1 2 3 4 typex
name2 3 4 5 6 typey
name3 2 3 3 1 typex
name4 5 3 4 2 typez
name5 9 8 2 1 typea