Thanks for the clarification. Build the hash exactly as you show. Process the keys with grep

use strict;
use warnings;

my %r_name = (
    a => [ 1, 2 ],
    b => [ 3, 3 ],
    c => [ 1, 6 ],
);

my @result = grep {$r_name{$_}[0] eq $r_name{$_}[1]} keys %r_name;
print @result, "\n";
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Result

b
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Note for next time: It is considered impolite to edit your post in a way that invalidates existing replies. Leave the existing text. Add a clearly marked UPDATE section.