Is this about what you're looking for?

for my $label (sort keys %family)
{
    my @names = @{$family{$label}};
    print "$label\n";
    for my $name (@names)
    {
         print ref($name) ? "\t@$name\n" : "\t$name\n";
    }
}
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Notice that you don't generally have to iterate through the index of an array. Note also that you were fetching an array ref into an array (@names). You need to dereference it, as I have done here.