my %hash_name = (a => 1, b => 2, c => 3);
my $max = (keys %hash_name)[0];
$hash_name{$_} > $hash_name{$max} and $max = $_ for keys %hash_name;
print $max;
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or using List::UtilsBy:

use List::UtilsBy qw{ max_by };

my %hash_name = (a => 1, b => 2, c => 3);
my $max = max_by { $hash_name{$_} } keys %hash_name;
print $max;
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