You can not do it with a simple hash.

Yes you can. However, that does not mean that you should :-)

my %h = ( 'aDobe' => 'abcd', 'big boss' => 'gcd', 'ADOBe' => 'abcd2' )
+;
my $str = 'AdOBE';
for ( keys %h ) {
   print "$h{$_}\n" if lc $_ eq lc $str;
}
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